Doppelganger's is new in Hellfire. You cannot get it in Diablo. According to Jarulf's Guide, the prefix Doppelganger's has a 5% chance to duplicate an enemy.[1] However, this is a per-hit chance, so the more times you strike an enemy, the more opportunities you have to duplicate it. Thus, getting a new enemy 1/3 of the time is plausible if your damage is low enough that you required enough hits per enemy. Doppelganger's is only qlvl 11, and has statistics equal to a Lord's (qlvl 19) prefix. You should probably avoid using a Doppelganger's weapon if your enemies are still a meaningful challenge, since the duplication effect will just make the fight harder. Switching to a weapon with lower bonuses, but no negative side effects, might be a better choice overall. On the other hand, if you are able to comfortably win these battles, you could look at the duplicated enemies as opportunities for extra experience and drops.

Also according to Jarulf's Guide, Doppelganger's cannot duplicate unique enemies, such as The Vizier.

[1] Two places in the guide say 5% (3.13.5, page 60; 6.2.1, page 139). One place says 10% (3.4, page 25). I choose to believe the 5% note, particularly since one of those is a step-by-step translation of the combat code.