I think I know what you're looking for, but I've never been able to find a generator that did exactly that. Making do with what is available depends on how you are going to use the names or words you come up with.
You might be able to find a word scramble generator that will let you enter parts of words and produce a list of combinations, but you will have to approach it as though you are creating a puzzle. A domain name generator (like the one below) might let you play with parts of words a little, but to a limited extent. I'd also recommend trying unique baby name generators (on sites for expectant parents), or, better yet, one that is meant to help writers or rpg fans make up character and place names; any of those might have generators or combination techniques that can help.
Really, the easiest way to play with custom combinations is by hand. Just write out parts of the words you're considering on little slips of paper and mix them up. Say them out loud and keep moving them around until you find something that sounds good to you. It's easy, quick, free, and might be just the thing to help you think of what you want.
Once you have some combinations that you like, it's time to do some research. Look in dictionaries for similar words. Enter them in search engines. See if they're similar to an unfamiliar term, or mean something in another language. See what's out there!
If you're really concerned about keeping the meanings of the words you combine, make sure you understand their etymological roots. I hope you find what you're looking for! :)