If I'm writing my 'About Us' page on my website, should I use the 1st person (me) or the 3rd person (my name) to talk about my artwork?
In short, ideally you'd use both.
The longer explanation is this:
If an editor comes along and wants to write about you in their newspaper or online or magazine, you'll want to have your details written in the 3rd person so that they can just copy and paste.
eg: Julie is an artist who likes referring to herself in the third person on her website, but only in the About section.
Whereas, if a customer comes along, they want to be more familiar with you, and they'll want to interact with you directly. That's when writing in the 1st person is much more appropriate, personal and involving.
eg: My paintings would look fantastic on that bare white wall you've been wondering what to decorate with.