Possible! It's a glitch that occurs. Nameless deer sometimes are shown having your picto. Yours is unique though, so don't worry. To other people, namelesses have their picto.

Yesterday I almost had a heart attack, because I saw someone playing as one of my deer. Same picto and set. O_O But when I logged off and came back on, it turns out it was only a no name. Gosh, I was glad that it wasn't a hacker.