There used to be such possibility in
partypoker years ago, then it was taken away, then restored again and then this famous mandatory change of all the nicknames came to make games more safe and fair, which was followed by the (*logic?!*) suggestion to make it real name games for every mtt. This idea sorta failed, so it was put on hold for a while (with some exceptions of course, as there are some RN tournaments and events).
Then rooms in MPN network gave such opportunity, but this network was closed last year.
All the others big rooms and networks don't provide such option, as far as I know. It might be a thing only if your nickname is obscene or reveals your personal info, but still it's to be communicated with the support of the room.