Well....the name could be very important, depending on who it is.
But, we don't know.
In the very broadest sense of "could be," yes the name "could be" important for our purposes at WS. But in any common sense scenario, no it's not going to matter. It's just a "who's he" of no importance.
Here's why.
1 Our purposes are about discovering the perp or perps who did this crime.
2 Knowing the name of who was in the car with MB doesn't tell us the name of
who personally killed MB, because that person could not have been in the car with BB. That's a fact.
3 Nor would we be able to know, just by knowing a name and a presence in that car, that the other person therefore plotted the murder of MB, if there was a plot.
4 So for it to be helpful, it would have to be someone whose presence would implicate BB as being a party to it. Right?
5 That offers only one scenario possible, in identifying that person's name, that would help us solve this crime, and that would be if it was a female with whom BB was having an affair. No other name would matter.
Now we've not heard that BB was actually having an affair, so there's that. But for the moment, I will ignore that total lack of evidence, work it from there, and see where it takes us.
That scenario says BB went to Biloxi to be out of town while he had his wife killed, took/met his mistress (that no one knows about) on the trip, and then returned home from Biloxi with the mistress in his car.
If all that is somehow true, then ...
(a) BB would have been hand delivering a motive and gossipy story to the media he knew was waiting for him, as they drove up. However, have we heard about him driving up with a woman in the car? Have we heard whispers that he took a girl with him? This wouldn't have been secret for more than a few days, at most, and the media would have had a field day chasing this, and making it into a major story, yet we've heard nothing like that.
(b) BB would have also been hand delivering the unknown mistress and the affair to LE, too, to consider in their investigation. No doubt they know exactly who he rode with, easy to find out as they arrived, and he would have known that.
(c) And since we're working on a scenario assuming that BB plotted the murder, we have an alibi trip he has planned to keep from looking guilty. Yet in this scenario, he takes someone with him on that alibi trip that is going to make him look guilty as can be, and rides back together with her, when the murder happens as he planned. What kind of alibi would it be where he had a girlfriend with him when his wife is murdered, to be seen by hotel clerks, fishing charter people, business associates, etc? And then also paraded her to his girls, media, and LE on his return, too? Does that make any sense at all? Of course not.
Take all that together, and we can be certain he didn't drive up with a likely-mythical mistress (the only person that would matter), nor is there any chance that LE doesn't know who he rode with.
And when we have ruled that sort of person out, naming any other name of a driver can't tell us a thing that matters for our purposes.