I have a secret naming panel that I use to help brainstorm names for companies without spending tens of thousands of dollars. But naming can be very tricky. As mentioned in the other answers, there is much more to consider beyond memorability and trademark.
A good starting point to do it yourself is to make three lists of single words: 1. function, 2. feeling, and 3. fun. Then pull back and look at those words. Do any go together? What speaks to you as the essence of your business? What synonyms do you find for each of those words?
I usually will work with my panel to develop a short list. That short list needs to be memorable, but also be relatively uncluttered with competitive search traffic and domains. An SEO strategy is a crucial part of this.
Hope that was helpful!
Happy to tell you more about my approach as well.