What strategies do you use to come up with names for a product? And is the name actually that important?

So, I've been working on my product for some months now and still haven't come up with a good name for it. I've tried combining words, using synonyms or words in other languages but I haven't been satisfied with any result. I consider myself a creative person but this task, in particular, has been pretty difficult.

I've started to wonder if the name is actually that important? If maybe I'm just thinking too much about it and would be better off by using whatever name comes to mind (of course related to the product or market I'm working on)

I'm not asking for name suggestions but rather I'd like to know the approaches you use or have used. I'm sure you have very creative ways to do this!

Thanks!