Sally Bullers left this question on the blog:
Is it legitimate to ask gallery owners for the name and address of those who purchase your art? I like to drop them a note and keep up my mailing list. Some galleries are very protective of these names.
You're right, Sally, some galleries are very protective. It's because they've been burned by artists who ended up selling directly to patrons or simply because they've heard of it happening to other dealers. You can eliminate a lot of the worry by negotiating with your gallery and nurturing trust in the artist-gallery relationship.
Yes, you should not only ask for names, you should have this arrangement built into your contracts with galleries. You need these names should something (heaven forbid) happen to your gallery. And your gallery should be able to trust you with them. (See links above for more.)
Image (c) Sally Bullers, Chase Away the Blues.