From the NameVoyager application at Baby Naming Wizard, the history of the name Caitlyn:
It first crops as a name for infants in the eighties and begins to become somewhat familiar in the nineties.
And of the name Zoey (the adopted name of the feminine transgender woman who physically threatened a wrecker who dared to state the biologically obvious fact that, gender identification aside, Caitlyn and Zoey are, biologically, both males):
Zoey first shows up in the nineties and still may yet to have peaked as a trendy name.
If these two had thought about becoming (or being, or whatever) women for their entire lives, one might expect that they would've long since identified names to represent their true identities, names that would've been popular when they were growing up, like Bruce or Robert.
If, on the other hand, transgenderism is the consequence of something else, like psychologically unstable men acting on a narcissistic desire to lust after themselves, we might expect them to pick names they had recently been exposed to from coming across hot teenagers or twenty-somethings with those names.