What to name a new graphic design store (online)?

[Jake]

All fo the good .com names are taken, you may find it necessary to compromise a bit to get an available name, by all means try to get a .com if at all possible.

There are sites with tools that help you come up with fictitious names, including: wordlab.com, naming.net, wordoid.com, lingzini.com, namestation.com, some of these tools look up the domain name availability as you go.
Any name not already used in a .com web site name is probably not trademarked.

You might be able to get expert advise in the wordlab forum?

wordoid tries to generate new words based on a seed word you provide, try looking through a few dozen results see if anything works for you.

Although the search rank benefit of keyword domain names is going down, it's still a plus to make a descriptive name, if not graphicsSupplier, graphicsKing would still beat coolLooks