All you have sent is a conversation between you and another member, unless there is a confession from the actual account this doesn't consitiute a ban. If you sent me a PM with the mentioned account holder saying "Yes I am littleD" it would be different, this is only speculation.
I will happily ban any account Little_D creates, but I WONT ban a member based on guess-work. Even if another member confirms this, this doesn't mean it is fact.
Also, until there is a reason to ban the account (except hearsay) there is no harm in keeping it active, if it is littleD they will slip up and reveal their identity in due course or commit a breakage of the rules.