Board Thread:The Panopticon/@comment-43908-20150311013943/@comment-6032121-20190210205552

That's one side of the issue, but another is that Romana [X] isn't in-universe. Per T:ROMANA we use it nonetheless for Romana I and Romana II, because that's what everybody else does; but for the two Third Romanas we have considerably more freedom, what with them being relatively obscure, and thus not really having any established usage about them.

Therefore, there is the fact that she only used the name Trey sparingly, yes; but there is also the fact that it is the name she chose, in-universe, to tell herself apart from another incarnation of hers. Whereas she's never gone in-universe by "Romana III", a name we're making up to, well, tell her apart from other incarnations.