Is it a good idea to name some mathematical objects after my thesis advisor?
It sound as though your advisor was not the first to study/define/use these objects, but rather you just want to name them something, and think it might be nice to name them in honor of your advisor.  Please don't do this.  You'll only contribute to Stigler's law of eponymy, confuse people, embarrass your advisor and/or offend whoever was the first to study these objects.

Bear in mind two things: (i) Not every random object deserves a special name.  (ii) When you name objects, name them in a descriptive and evocative way, that will make using the terms intuitive and non-confusing (as a corollary, it also shouldn't conflict with other notation).  Many people don't even like the idea of name any mathematical objects after people, though it's common practice.

Now that naming them after your advisor is out of the way, you should feel free to consult your advisor on naming these things.