But again, the notion that NX-01 was called “Dauntless” before the Borg First Contact incursion is your headcanon. No one working on Enterprise ever attested to that, and Cromwell’s casting as Cochrane is certainly not evidence of this alteration.
You started this conversation by saying “They did the same thing for First Contact” and I just want to know who “they” is and what the “same thing” that “they did” is. You’ve brought up this Dauntless/Enterprise theory twice now but that’s certainly not evidence that any “they” did any “thing.” As far as I can tell it is your headcanon for a relatively minor inconsistency that could have any number of other explanations, the most obvious one being that Arturis got a detail wrong.
I just find it incredibly hard to believe that anyone working on Enterprise was working on the assumption that they were creating a show in a timeline that was “altered” by the events of First Contact. That was never alluded to in the show’s four year run and as far as I know no one working on that show ever said anything of the sort.