Start with how it feels
A name should be comfortable to say, straightforward to spell and suitable for the business you want to build. Try it in a sentence, an email signature and on a small screen. Ask someone unfamiliar with it to read it aloud.
Give yourself room to grow
Consider whether the name fits more than your first product or service. A name tied to one place or activity may be right for you. Make that choice deliberately.
Keep the checks separate
Company-name, trademark and domain checks answer different questions. A positive result in one does not settle the others. Search results can change and do not reserve a name or guarantee registration.
Your next small step
Write down three options, why each fits and which checks you still need to complete. Use the official Companies House name checker as one part of that process.