That is a glitch, I don't think someone would break into an account especially if it has difficult password.
This one is a glitch that appears at nameless deer, non-registered users of the game. They don't have their own pictogram so they have to "borrow" others'. Everyone sees them with their own pictogram and at times also with pictogram of the player who right away left the game, or picto of one of the Creators. They mostly have gen1 pictos borrowed. They can play as fawn too.

And sometimes a creepy glitch can happen, I mean creepy. I once found a deer that had the same set and picto as mine hopping around happily. I was sure it couldn't be hacker, thought, as my password is longer than the password field (srsly). It turned out to be glitch of the server. Or I have once seen my very own pictogram on the map and hadn't bothered to jump in and check it out. I found a deer with the same set and picto again... And I was proved that others can see these creepies too.
Or if your game crashes and you rejoin it fairly quickly, you can sometimes leave your clone behind. Those can be seen by others too and can last for quite a while, it happened to me many times and twice people behaved to the clone like it would be me. Nuzzles, keeping company. I was all OMG. But that was just to let you know.

I know, too much text maybe but yeee I want to help ^^

Do un-named deer show up as fawns, though? I could have sworn Doppelganger Friend acted the same every time we hung out as fawns (only two or three times but still).

For the adult "doppelganger" it kind of makes sense; that deer acted differently, too. And I guess if they were un-named, then they couldn't tell they had the same pictogram.

'Nameless deer' are deer who are playing the game as a guest. They appear as adult deer and do not have the option to play as a fawn. They should appear as deer without a glowing pictogram, but frequently the server will populate 'nameless' deer with either a random pictogram, or your pictogram. Usually anyone seeing the nameless will see their own symbol reflected back at them, but sometimes others will see your symbol.

Don't worry, this is a very common glitch and does not mean someone has access to your account.

In the case of this fawn, it isn't likely someone playing as a guest (because when you play as a guest the open to 'play as a fawn' does not appear in the menu) but it could be another player who's pictogram has gotten mixed up by the server. They are likely seeing their pictogram not yours. They could even be seeing your pictogram as their own! The game is very glitchy when it comes to pictograms, even among registered 'named' accounts.

edit: Just let me verify that this is true, I want to make sure nameless deer are unable to play as fawns.
edit2: The option to play as a fawn only appears when you have logged in with a registered account. Therefore nameless, unregistered players could not appear as a fawn.

I stand corrected, thanks Pega! I've never seen that before, t seems like TEF gets more glitches with each new generation of pictograms lol getting hard to keep track of them all.

I have seen that glitch too many times but one time I confirmed it. My brother and I both have computers and they are in the same room. He was going to play as a nameless deer and go up to people and dance and so I wanted to be funny too so I stayed as my character and just turned into a fawn. Then he got bored and wanted to see if spells worked on nameless deer so we met at the pond and that was when I saw it. He was a fawn on my screen and he had my pictogram but on his screen he was an adult with no pictogram so we confirmed it. When you see a nameless deer and you are a fawn it will appear as a fawn but if you are an adult it will appear as an adult.