Here are just my thoughts and guesses based on what we now know.
I am going to work under the assumption Marlyse was Elizabeth Evans. A lot of people who know this case better than me have long speculated the oldest victim might be Elizabeth Evans because of the timing, the fact that there is no other likely candidate for Elizabeth, and the isotope evidence that the victims lived in New England before their deaths.
Marlyse having the middle name Elizabeth now makes that case a lot stronger. In fact, I'd argue her first name being Marlyse is also further evidence for this theory.
We know Terry Rasmussen was still calling himself Terry Rasmussen as of November 1978. Within a year or so, he would be calling himself Bob Evans. I will discuss later the different possible motives for him abandoning his birth name, but clearly he wanted a new identity. Not just a new identity, but a more generic identity.
Compare the name Terrence "Terry" Peder Rasmussen to the name Robert "Bob" Evans. Terry Rasmussen is much more memorable of a name. Terry Rasmussen is a guy who's probably pretty easy to find, if you're determined to look. His middle name is spelled in an unusual way, even if his first name is more common. Bob Evans, on the other hand, that's a forgettable name. That's a guy who's hard to find. If you go looking for Bob Evans, you'll turn up hundreds of people just in one state.
Now let's also look at Marlyse Elizabeth Honeychurch. Doesn't seem like there's *anyone* else by that name. Maybe Marlyse was a more common name in the '50s than it is today, but I haven't ever met a Marlyse. I've met plenty of Elizabeths, though. Elizabeth Evans is, like Bob Evans, an extremely forgettable and generic name.
As for why the name changes, there are four possibilities that jump out at me:
1. Something related to the custody situation with Marlyse's daughters. It seems like before her disappearance, their fathers were involved in their lives. Maybe one of them objected to Marlyse's plan to move across the country. Sarah's father had physical custody of her not long before they disappeared. It would make sense, with him being in the military, that he might've turned primary physical custody back over to Marlyse, but there's a huge difference between giving her primary physical custody (especially of a child who isn't in school yet and who's schedule can be more easily divided 50/50) and being okay with her taking their daughter too far away for him to regularly visit.
2. Something related to the custody situation with Terry's daughter.
3. Terry had murdered the mother of his daughter and was worried he might come under police suspicion.
4. Terry was concerned about being implicated in a totally different disappearance or murder.
I also think it's likely that Marlyse was motivated (and thought Terry was also motivated) primarily by reason 1 or 2, but Terry was really secretly motivated by reason 3 or 4. Whatever the reason, I suspect the name change was Terry's idea and he persuaded Marlyse to start going by her middle name rather than her more unusual first name. The last name change could've been just blending in more, but also probably stemmed from a marriage that wasn't legally binding like he had with Eunsoon Jun. He did list Elizabeth Evans as his wife, after all.
Well, it's already been speculated that if Elizabeth Evans was one of the victims, she was probably murdered between May and October of 1980, since in his arrests in February and May of 1980 he lists Elizabeth as his wife, but then in October 1980 he doesn't. I've seen it pointed out in the past on this site and others, again by people who know this case better than I do, that this timing could make sense with at least one of the children attending school, and Terry deciding to kill them over summer break to avoiding arousing suspicion. If one of the children was in school, this might've been a necessary precaution since Terry wanted to remain in the area, and did remain in the area for more than a year afterwards. The timing of when he would've had access to that location also seems to work with this timeline.
So a question I think amateur sleuths need to look into was whether or not Marie was in school and whether or not the middle child was in school. In order to keep a low profile, Terry might not have wanted the children in school, so of course it's a possibility that neither of them were. But there's also a possibility this could be the key to the middle child's identity.
I think there's a fair possibility Marie was enrolled in school. Assuming she was in school in California (and it would be unusual if she wasn't) both Marlyse and Marie herself would likely expect she'd be in school in New Hampshire. It shouldn't be too complicated of a matter to check the location Bob and Elizabeth Evans were living in during that period in early-to-mid 1980 and see what elementary school they would've been zoned for. Assuming NH had a similar age cutoff to what I'm familiar with, during the 1979-1980 school year, Marie would've been in second grade. I would also check first and third grade yearbooks to be sure.
There's of course the question of what name Marie would've been enrolled under. I doubt it was Marie Vaughn. Given Marie is a pretty common first name, and the difficulty of explaining to a child why she has to start using a new name, I think the first name might've been Marie. The last name may have been Evans, or it may have been another relatively common last name. Or it could've been something totally out of left field. But if she was in a yearbook, now we know exactly what she looked like and she shouldn't be hard to spot. If we know what name she was using and what school she was enrolled in, that opens up the door to finding children she may have known, and those children or their parents could be invaluable resources to finding out about Marie's life in New Hampshire and, crucially, the name of the other little girl who lived with her.
The middle child herself was probably too young to be enrolled in school, but I still think it could be worth looking into. See if there's a little girl who was in Kindergarten who resembles the image we have, or who was using the last name Evans. There's also the possibility, if she was born in 1975, that Terry was supposed to register her in school in the fall of 1980. Maybe he didn't want to do that? If she were enrolled in school, there would be greater scrutiny if she (or the family as a whole) just disappeared. With a step-daughter, Terry could always tell people her mother just left him and took her out of state. But with his own daughter it might be more complicated, especially if he'd told people he was a widower, as he did later when he was traveling with Lisa. Maybe his daughter's birth had never been registered at all, and while I don't think that would've been an impediment to putting her in school during that era, he might've hesitated to finally make her existence a matter of public record. He also might have been concerned with the middle child, and possibly Marie as well, telling their teachers things that could get him into trouble. Whatever his reasons, this might've been a point of contention with Marlyse. Whether either child had attended school in New Hampshire before or not, if September rolled around and he refused to register one or both of them for the new school year, that would probably have spurred on a conversation he didn't feel like having.
Another thing that fits well with a timeline where Marlyse was Elizabeth Evans and the victims were killed over the summer or early fall of 1980 is the fact that Terry Rasmussen made no distinction between his biological daughter and Marlyse's daughters. Not just in the fact that he killed them, but the timing and circumstances of their murders and where he placed the bodies. It almost goes without saying that he was incapable of loving his daughter, or being a father to any of the three girls, but if he hadn't known Marlyse or her children for very long, it's harder to imagine him deciding to kill his daughter who he presumably had raised since birth, at the same time for the same reason.
This crime makes sense as a type of family annihilation. Rasmussen selfishly decided he did not want to be in the role of husband and father anymore. Perhaps there was an argument with Marlyse that spurred it on, perhaps she was planning on leaving him, perhaps she wanted to go to the police over him abusing her or one of the children or some other crime he had committed. But ultimately he decided to murder not just Marlyse but all three children, two of whom were probably not old enough to be witnesses against him. If he had been with Marlyse for about two years, from 1978-1980, it would make sense for him to see them as a unit. If Marlyse had raised and loved his little girl along with her own, it makes sense that he would murder all three children together, at the same time and place, probably for the same reason. Tragically this type of crime is much more common than it should be. This aspect of the crime makes a lot less since if his relationship with Marlyse was more fleeting or if he'd spent less time with her children.
I think we now also have a crucial piece of information when it comes to finding out the identity of the middle child: that Terry Rasmussen was in Southern California using his own name as of fall 1978. Not just legally using his own name, but socially as well. It's hard for me to imagine him switching to another name and then resuming using his birth name, so that is probably the name he was using with his daughter's mother and her family, and they may have lived somewhere in that area around that time. It also makes a lot of sense now to work under the assumption that his daughter's mother was the woman who his older children met in 1975 or 1976. With all of this circumstantial evidence put together, I think we could be very close to the final piece of the puzzle.