If you need a quick-and-dirty stamp, get a sheet of craft foam (it's usually thin and comes in tons of colors). Cut out the pieces you need (or as one large piece) and glue onto a hard surface, like a wooden block. Fast and cheap! (not good for small details though)
BTW don't dip your stamp directly into the paint, because that will get into crevasses and make the resulting stamped image look messy. Getting a stamp pad would be best, and doesn't cost much. If you're desperate though... get a sponge, dip it in your paint, wipe the excess on a sheet of wax paper, then lightly tap the stamp against the painted side of the sponge. It's messy, but it all depends on how desperate you are.
But like shininginthedarkness said, linoleum blocks are commonly used for stamping. Those do need special tools and it can get a bit pricey. If you need a stamp that will last, this is your better option. And yeah, you usually use a breyer to apply printing ink onto the linoleum block.
If you just need a name, maybe check out local printing places to see if they do custom stamps. For example, in the US places like Office Depot have a print/copy center that can make custom signature stamps for as low as less than $20.
Thanks! I'd be keeping an eye out for the local printing services if they've such services. Most I've come across seems šustome'made'for printing bussiness addresses, no pictorgrams stuff. Still its an alt