I'm a big fan of brainstorm sessions. When I named my business I looked at things I wanted, something fun and personal to me, but something that wouldn't look bad on a business card.
I make a list of names in the same field that I like - is there a pattern? (IE: Do they all say 'productions', 'firm', etc at the end of it) Or, do they all have similar words?
A thesaurus can be great. Make a list of everything you want your business to say about you. Take the thesaurus and see what other words describe those things.
Once you have brainstormed, try to have at least 5 solid ideas and variations of those ideas.
Look at that list.
Will anything make you seem unprofessional? It's great to have a fun name but if it takes away from your skills then it's a big no-no.
Will it be easy for people to remember? (Not only the name but is it easy to spell and can they find the website easily by the name)
Google the name.
Is it very common or too similar to other names? A unique name that is simple will be easy to google and hence easy to find for your clients.
Always remember KISS - keep it simple stupid.
If it's too complicated, too long, too difficult to say, to write, then it's probably not the best idea.
Make sure the name presents a clear concept of who you are, what you do and presents you in the best light possible.
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