Could a loner or kittypet be invited into a clan and then denied entry because they didn't want to take a clan name?
It depends on the Clan culture and leader's personality at the time. More often than not, a Clan will accept a newcomer not wanting to give up their name, though with great reluctance and occasional verbal pushes to take on a warrior's title regardless. Sometimes the cat is given the choice to leave or accept their new culture's rules, and if they refuse a rename, they are escorted out of the territory with some polite force.
The thing is, Clan cats understand the personal importance of a name - it's the most significant aspect of the average warrior's life. There are, at minimum, two ceremonies just for naming that every single cat will go through, and at max, you may have five (kit-to-apprentice, apprentice-to-warrior, injury rename, leadership, and retirement, thus losing leadership). It's a big deal, basically.
So, though they still believe their culture is The Best Culture And Everyone Should Live By It Completely If They Join Us, a good three-quarters of Clan cats will get it if a newcomer's hesitant. They may not agree, but they get it. They'd want to keep their names too, no matter where they end up. Sure, your name is silly to them, but it's your name, you know? It's a hard place to be in! That warrants sympathy, most think, and thus patience. Maybe you'll change your mind later, when you're more comfortable. Until then, you'll be called your original name, and we'll only occasionally suggest you comply with the Clan's wishes. That's fair, they think.
