ShawN shawN • Good question Yoram. I think your response depends on how reputable the gallery is. Why is that? If you have a good relationship, then giving them contact info on customers, they could expand your sales at existing customers if you continue to sell with that gallery. Some artists are very fond of their galleries like Gehardt Richter.
Another take is if you have little confidence in the gallery or you believe they are not representing you well, then yes, I would keep the list. If you have such a bad relationship with the gallery, then why are you even selling there?
A third take is that this is a gallery in business to make money. By giving a reputable gallery or proven gallery your customer list, they should be able to drive sales from them and their friends. Additionally, any 3rd party selling your work needs to be paid, so there will be a commission. They cannot stay in business otherwise and generally should multiply your sales vs. steal sales. I personally tripled my sales price going to a gallery.
If you have an art show, you should promote the show to your own contacts as well with your own invitations and not depend solely on the gallery. Hope this helps!