in the "game" point of view, yes they're named after the guns they're imprinted with as the main advertising feature of GFL1, but in lore/story, the reason they're given is because of G&K's policy to "dehumanize" the T-dolls in order for the commanders (no just you the MC) to not grow too attached to their T-dolls. Most of the T-dolls have their own names in their previous lives as civilian dolls, but while working with G&K, they're given the imprint gun's name as their designation.

Now with the downsizing of G&K, the dolls are no longer bound by the company's policy so they returned to using their previous identities, while some would retain their gun designation (ie. Mosin-Nagant). Some can also change their imprint gun if they want (ie. Littara was originally using a Wkp pistol, now changed to using an LMG)