So this is really a personal preference and not hard and fast canon, although I do believe there is strong canonical evidence for this opinion, but: I don’t think Leopold Fitz goes by Leo. Ever.

We have heard characters use first names for Jemma, Melinda, Phil, and Grant. However, even in the most intimate of settings, where Fitz will call Simmons by her first name, Jemma does not. She still calls him Fitz. It’s understandable that they generally use last names, since SHEILD/the BUS are professional environments. However, it’s clear the team has become a family, and they do use first names when they want to explore those personal relationships: except no one has ever called him Leo.

In fact, the only time we’ve heard his first name is in Seeds when Agent Weaver introduces him. And even then, it’s “Leopold Fitz” and not “Leo Fitz.” It isn’t hard to imagine that Fitz dislikes the name “Leopold” in general, since it’s a pretty… interesting name. It isn’t hard to imagine Fitz letting his Mum call him that because she’s his Mum. Maybe Ms. Fitz uses “Leo” to be affectionate.

But given a choice, Fitz prefers Fitz. Not Leo, and definitely not Leopold. Maybe I’ll be proven wrong, but even then I’ll find it personally cringe-worthy: Fitz’s name is a very important part of his identity and personality. “Leo” doesn’t fit him, and I think he knows that, and sticks with Fitz.

There are people who just go by their last names. I truly believe Fitz is one of them.