Generally these are called holders. Cup holders for pens. File holders for pens. Multi-hole holder for pens.

I think pen holders, and more specifically, cup holder for pens, are the most common ones. The rest that have been suggested aren't so common.

I would call all three of them "pen holder". I might call 2 and 3 "pen organizer", because you can sort the pens by type and not mix together as in 1. 3 can also be called a "pen rack", I think, but I don't think it's very common. I've never seen one like it before.