Bad nicknames are forbidden in Islam.
And do not insult one another and do not call each other by [offensive] nicknames. Wretched is the name of disobedience after [one's] faith. Qur'an 49:11
Though good nicknames prevail, Just like the one of great Sahabee Abu Hurayrah [pbuh].
Some people keep their own nicknames. If they are good, let them prevail but some keep bad ones like Serial Kisser, etc. Some people including women give themselves very hateful and vulgar nicknames. This practice is too common on the internet and when asked they cite the reason as anonymity.
Good or bad, are muslims allowed to choose nicknames for themselves in this way?
References to scriptures would be highly enlightening to all.