I've started to write my first Fantasy novel. But there's one question that always bugs me. If I were to have a Kingdom, of course I would have a fictional name for it. So if I have a non-fictional place in my first few books, can I have a non-fictional setting later on in the series?
Fantasy literature is full of examples of characters passing between real and imaginary worlds. It is one of the core theme of fantasy literature. Indeed, the roots of fantasy literature are all in the long folk tradition that has seen a magical world existing side by side with the real world, and with passages between those worlds, in both directions.
I think it is probably fair to say that the fantasy that happens entirely in an invented world a la Tolkien is probably a very recent thing, at least as a dominant form of the art. It wasn't something his contemporaries practiced. C.S. Lewis' work was all about children passing from England into Narnia. Charles Williams's books (which deserve to be far better known than they are) were all about incursions of Faerie into the real world.
Alan Garner, Susan Cooper, Madeleine L'Engle are all examples of writers who work was about the border between worlds and transitions between them.
In short, no, there is nothing to prevent a transition from the real to the imaginary world. What you do have to be careful about, though, is maintaining a consistent overall tone and mythos. If the transition comes out of the blue and upsets the order of the story world, you are likely to lose your audience. Foreshadowing is your friend.
"So if I have a non-fictional place in my first few books, can I have a fictional setting later on in the series?"
If you mean, the first three books in the series are rigorously historically accurate historical drama set in, say, Britain, and then in the fourth book the characters head off to the Land of Oz, this could be very tricky to pull off. I can enjoy a historical drama like Downton Abbey. I can enjoy a science fiction story like Star Trek. But if on the fourth season of Downton Abbey the characters were beamed aboard the Enterprise and headed off to another planet, wow, that would have to be done VERY skillfully to work. Most likely I'd say "oh give me a break" and turn it off.
Jumping from one genre to another is possible, but very hard to pull off.