I don’t actually know if there’s a good way or a bad way to come up with the name of a brand but I do know one thing: you shouldn't waste too much time coming up with it.
This is exactly what we did to arrive at the name of our in-house brand, Orin:
1) Have each person on the founding team come up with ~5 names.
2) Narrow down the list to 5 by having each person vote for their top 5 that is not their own.
3) Find potential domains for each of the names.
We used Shopify’s Business Name Generator Tool to figure out what domains were available.
4) Send out a survey to friends and family.
We created a quick survey on Google Forms describing what the brand will be about and asked our friends to choose their favorite name.
These were the results:
Overall, it took no more than 2 hours of work over a span of one week to finalize the name - I'll call that a success.