If creatures you control deal combat damage to more than one player at the same time (most likely because it's a multiplayer game), Pyrewild Shaman's ability will trigger once for each of those players. However, only the first such ability that you pay for will return Pyrewild Shaman to your hand. Even if it's put back into your graveyard before the other abilities resolve, it's considered a different Pyrewild Shaman than the one whose ability triggered.

Pyrewild Shaman's last ability triggers only if it's in your graveyard when the creatures deal combat damage to a player. Notably, if Pyrewild Shaman is dealt lethal damage at the same time that a creature you control deals combat damage to a player, Pyrewild Shaman's ability won't trigger.