Once your hero reaches level 18, you shell receive the following message:
Your hero is finally mature enough to start being responsible for someone. No, no, he is not going to marry, at least not now. But it’s very likely that he’ll get some “company” soon. Maybe he will get a pet from a local pet store or tame some abandoned monster or even a hero. Pets can be very useful in heroic undertakings. On a side note, heroes need to take care of their pets, otherwise pets can leave or even die.
'Pet system is currently unavailable in the English version.'