for example: if you found a cat without a name, then, if you name it you can have it. - another example: if you want to do something out of names, you should use (say) if you say it, you can have it. it means that you can have whatever you speak. if i speak/say it , can i have it?

If I name it, can I have it? Now I want a pizza.

The sentence is fine. But whether using 'name' is "weird" or not would depend on the context. Can you describe the context?