I've noticed that a lot of fellow furries will refer to each other by online handles or fursona names, even when meeting in real life. My roommate who I met online has lived with me for a year and a half now, and she still does this with me.
It's only recently that I started meeting people from the fandom in real life, and it always was a bit weird to me when they referred to myself or someone else by an online handle (but it doesn't bother me enough to correct them). Growing up, I was always taught that the purpose of online handles was anonymity - to prevent yourself from being identified in real life by those who may have ill intentions for you. In that context, using them in a face-to-face meeting can come across as silly. We already know enough about each other to meet up. Odds are, we know each other's real names and a good deal about each other. We aren't on a website where we need to protect each other's anonymity from third parties. So, why does it happen?
I think it comes from the fact that for many of us, our online identities are a way to more authentically express ourselves in ways we don't feel like we safely can in most contexts. In that context, continuing to call someone by their online handle can be seen as a gesture of mutual belonging and acceptance of identity, rather than distance and anonymity.