Start with the work the name must do. Write one sentence about the people you help, the problem you solve and the feeling you want the brand to leave. A short brief gives a team a shared standard and makes brainstorming less random.
Generate across a few directions: descriptive names that explain the offer, suggestive names that point to a benefit, and invented names that can carry meaning over time. For every option, check whether people can say it, hear it, spell it and remember it after one exposure. Ask people who resemble your audience what they understand without coaching.
Build a shortlist before falling in love with one option. Search the web, app stores, social handles and relevant business registries. Check the matching domain and compare registration with renewal prices. Availability can change, and a domain check does not establish trademark rights.
Write down why each finalist works and what it might confuse. Then research trademarks in the markets where you plan to operate and seek qualified legal advice when needed. Treat generated names as prompts for that research, not as clearance.