I personally, use a mix of fantasy and existing. Sometimes I form the fantasy from the existing.

Given that I map mostly for stories and other projects I'm working on, my places have a whole history and what not. So, for example, when I'm working on a story that uses ancient Greece as a base, then some things can be tracked back to that time/world. Also, I think about what I name things. Whether that's a city, a building or an entire world. It needs to have meaning in my opinion.

For my world 'Kentro' (set in a fantasy galaxy), I looked up the word "center" or "middle". This is a world directly from the Greek language, given that I used ancient Greek as a base for this world. Kentro literally means center. I used that word because the inhabitants of that world really think everything revolves around them. They consider themselves to be the center of the galaxy.
Sometimes though, I just look up words with a certain meaning and brainstorm next on a fantasy word.

Currently I'm working on a world with several races, so the names will have different origins. Based on what background I give the creatures. For example, if I base a Dwarf society on old Germanic society, I will dive into that history and get my inspiration for everything related to my Dwarves from that time of our history.

I will never stop using my own imagination, but I will make sure that things don't get mixed up. Even a fantasy word must <i>sound</i> like it comes from the same language as the others. Whether that's a made up language or not, whether it's a fantasy word or not.

As for the order of naming things:
I don't really name things in a specific order, really but I usually start with the inhabitants of the world. Given that they in the end named their world, if you want to have a plausible story. If I use several races, there'll perhaps be several words for the same thing.
After that, I tend to run from big to small and back again. First the most important things/places/objects in the world and then work to the smaller, less important things.

Sorry for the long post, and I hope it's all clear :'D
~Cee