Again, just personal opinion here. I always felt that the NX-01 was named "Enterprise" at the request of Zephram Cohrane as a tribute to the folks who helped out with the first warp flight.
And that in the "original" timeline it was the "Dauntless". This would "explain" it being missing from the "Enterprise" models in Picards ready room or the pictures we saw in "TMP".
Which is consistent with the idea that the events of FC created a divergent timeline. You could even say that the work of the engineers that assisted Cochrane subtly influenced technological development. This further is supported by things like references to the Admiral's beagle and the presence of a ENT ship in the debris in Trek 11.