As you said multiple staff members were telling you to change your gang name as it was too similar to the gang name "Azgeda", when staff told you to do this you proceeded to not co-operate with as you had clearly had no intention to change it, you were then jailed for 10 minutes which staff told you that you had the remainder of the jail to do so.

Regarding your ban you had enough recent punishments on your rap-sheet to be banned for a short time as can be seen here;