Depends on the variety - some are self fertile

Most European plums--Damsons, Prunes, or Green Gage--are self-fertile. With a few exceptions, listed in fruit growing books and sites, Japanese plums need a different variety of Japanese plum nearby to pollinate it. If you are short on space, plant two varieties in the same hole, and keep your pruning shears handy to keep one variety from taking over. After a few years, the roots will graft, and it will act like one tree with two trunks.