Anecdotal, but I've heard this too. I just tried with variations of your same prompt on arena.ai, across three different battles (i.e., six LLMs answered, in total.)
Each provided an identity in the first turn, something that they won't do as readily if asked in plain English, and in each case the answer matched the model ID as disclosed by arena.ai after voting -- except in cases where the model ID was a masked/hidden one and then I just had to take it on faith that the model was what it said. (I didn't have much to vote on, but I ended up voting for the answers I felt provided the style, content, and length I was expecting.)
Each provided an identity in the first turn, something that they won't do as readily if asked in plain English, and in each case the answer matched the model ID as disclosed by arena.ai after voting -- except in cases where the model ID was a masked/hidden one and then I just had to take it on faith that the model was what it said. (I didn't have much to vote on, but I ended up voting for the answers I felt provided the style, content, and length I was expecting.)