Naming a business versus naming a product: two different tasks!
Keep the business name general/vague enough that you can add new products without a mental disconnect between the busienss name and the new stuff. Give the product a more specific, more "grab-you-right-away" name. I like the MS Word thesaurus function for brainstorming lots of words, which you can then recombine to get something original. When brainstorming, don`t forget about verbs and adverbs. Nouns and adjectives are useful and nice, but not everything. Think of your favorite movie character who needs one of your products (or embodies their qualities), then verbally describe that character.
Ask yourself some of those new-age-y questions, like "what COLOR is the MOOD of my product?" (not what color you are making them) or "what ANIMAL would enjoy my product?" or "WHERE will people think to use this product that I wouldn`t expect?" and see where that takes you. Don`t forget about translating into another language.
If you don`t consider yourself a great brainstormer, recruit some kids to help you. They are such flexible thinkers that they can really surprise adults. Plus you won`t have to worry about non-compete agreements!
Good luck with your wordplay.