What name is given to someone who collects beach stones?

Answer 1

I call myself a rock-hound when checking the shapes, patterns of lines and cracks, and different types of rocks compressed together on Manitoulin Islands North West shoreline. Glacial movement of years gone by created very unique and different sized stones and boulders here. Its a rock-hounds picnic area.

Answer 2

Beach stones are still a type of Rock. Someone who just collects rocks as a hobby can only be called a "Rock Collector". You could get a little more imaginative and descriptive and say "Beach Rock collector".