Revisiting this timeline:
Terry Rasmuseen timeline: Suspected serial killer's time in NH, across country
From what is known, it is possible that Rasmussen and the Unknown mother were living in Texas when the UID child was born. (Possibly in 1976). Also, it looks like he was pretty much using his real name up to 1978 or 1979 when he appears in New Hampshire as Bob Evans. It could be that he changed his name because of what/whatever happened to/with Unknown Mother or to hide from her because he took the child. Just a thought.
As others have speculated, I think Honeychurch was the woman using the name Elizabeth Evans and her and the girls were murdered between May and Oct 1980. From that point on, Rasmussen regularly took on new identities.
1975
June - Rasmussen is arrested in Phoenix for aggravated assault. It is believed that his wife and children left him shortly after the arrest.
1975 or 1976
December - Rasmussen visits his family unexpectedly in Payson, Arizona. He was with
an unidentified woman, who police are still hoping to track down. He told his family he was living at the Casa Del Rey Apartments in Ingleside, Texas. His family never saw him again.
1976
January - Honeychurch and her daughter (Marie) are believed to be living in Santa Ana, California.
1977
Dec. 13 - Honeychurch's second daughter, Sarah Lynn McWaters, is born.
1978
At some point during the year, Rasmussen contacted a friend in Arizona, asking for money. He said he was working in Texas on an oil rig.
June - Rasmussen works for the "Brown & Root" Company in Houston, Texas. Records there indicate Rasmussen quit the job to work elsewhere.
Sept. 28 - Rasmussen's divorce is finalized, but his whereabouts are unknown.
November:
-- Honeychurch was last seen by her family on Thanksgiving at her mother's house in La Puente, California.
-- Honeychurch introduces her family to Rasmussen, who reportedly goes by his original name. This the only time Rasmussen has contact with Honeychurch's relatives.
-- Honeychurch's family believes she left with Rasmussen and her two daughters.
-- Rasmussen did not bring any children with him during his visit to La Puente, California.
-- Honeychurch had an argument with her mother and her family never saw her again.
1978-1979 (approximately)
Rasmussen works as "Bob Evans" at Waumbec Mills as head electrician. (New Hampshire)
1980
January - "Elizabeth Evans" -- who has never been located or identified -- signs a certified letter in Manchester, New Hampshire. Rasmussen is associated with the same address.
February - Rasmussen is arrested in Manchester, New Hampshire, as "Robert T. Evans" for issuing a bad check on Dec. 21, 1979 (insufficient funds). "Elizabeth Evans" is listed as his wife on the arrest report.
May - Rasmussen is arrested in Manchester, New Hampshire, as "Robert T. Evans" for theft of services (electricity). Rasmussen's spouse is listed as "Elizabeth Evans."
October - Rasmussen is arrested in Manchester, New Hampshire, as "Robert T. Evans" for diverting electric current. Rasmussen's spouse is not listed on this arrest report.