So I decided to look up some Alexa data on what keywords drive search traffic to several artists I know are successful and selling their art.
Note that the bars indicate the volume of search traffic, so, in each case, only the top 1 or 2 terms really seem to be sending a significant percentage of the traffic.
Top keywords sending search traffic to Kevin Macpherson: "kevin mcpherson", "kevin macpherson artist", "kevin mcpherson", "kevinmacpherson"
"Branded" keywords sending search traffic to Kevin Macpherson in report: ALL
"Generic" keywords sending search traffic to Kevin Macpherson in report: NONE
Top keywords sending search traffic to Richard Schmid: "schmid", alla prima, alla prima book
"Branded" keywords (out of top 10) sending search traffic to Richard Schmid in report: 9 (alla prima, stove prarie press are Schmid brands).
"Generic" keywords (out of top 10) sending search traffic to Richard Schmid in report: 1 (sign lithographs)

Top keywords sending search traffic to Hazel Dooney: "hazel dooney", "hazeldooney", "dooney", "hazel", "hazel in decent" (what is that one about?)
"Branded" keywords (out of top 10) sending search traffic to Hazel Dooney in report: 9 ("dangerous career" is a Dooney "brand" form the "Dangerous Career Babes" artwork series).
"Generic" keywords (out of top 10) sending search traffic to Dooney in report: 1 ("ultra violet one")
Overwhelming top keyword for Kevin Macpherson? "kevin mcpherson"
Overwhelming top keyword for Richard Schmid? "schmid"
Overwhelming top keyword for Hazel Dooney? "hazel dooney"
What do you think the overwhelming top search term for people coming to your artist web site will likely be?
Sincerely,
Clint Watson
Software Craftsman, Art Fanatic, Contrarian Marketer
via clintwatson.net
Then "Lori Woodward artist"
I also get a lot of hits for "Putney Painters"
But most of my traffic comes through links from Facebook, Twitter, Fine Art Views, Artist Daily, other artists who put links to my blog on their site.
Brian Kleiwer had an interesting point about search words - he put Farnsworth Museum on his site because he lives near there and it's an art museum. That got me thinking that I should put meta tags on my site saying "Acadia National Park" and "Tucson Arizona" because I paint those places, but maybe that's not connected to what you're asking Clint.