My seeds are almost entirely OP. The only exceptions are a couple of plants I have that never seem to set seed unless I help them out, but the pollen generally comes from whichever plant in the garden actually has some when I need it. Now I guess I could keep track, but that's too much trouble.
As far as the names, no nothing is registered. I just give them garden names if I decide to keep them. So, yes someone could come along and use those names.