How about something simple like ...
" 'your name's airbrush tattoos"
Or Something cool like ... "East coast airbrush tattoos"
or ... if you are a girl... "Angels Airbrush Tattoos"
Also you could always use "temporary" instead of "airbrush" if it helps with your name.
I think to advertise properly (you are planning to have your name on signs arent you) it would have to contain either "airbrush tattoos" or "temporary tattoos".
I never named my business anything, just my "name" and "airbrush tattoos". Then I bought 2 big banners with the words "Airbrush Tattoos" on them. (http://www.theweekendworker.com to see it)
I can see why you want a name though... it looks and sounds cool and you will start to build a "brand" so to speak.
Try a name that uses alliteration. Like the one above which was "Angels Airbrush Tattoos" or "Tiki's Temporary Tattoos".
Here is a tidbit of info from another question asked on wikianswers about alliteration:
The answerer said
"Alliteration. Repetition of initial consonants or sounds is alliteration, and is very handy for emphasizing a certain phrase, or as a memory aid."
The memory aspect is what you are after with your business name. If you set up at an event with 2 other airbrush tattoo artist's you will want to stick out, or at least keep your loyal customers, which is will be easier for them if you have a good memorable name.
Hope this helps
Ps You probably don't want it too long... banners are only so big!