As said above, IF you change your name your weapon licenses will be removed.
-You got two solutions.
In Characterly I thought you copied applications since IC-ly I didn't know you changed your name and that's why you got banned from applying for two weeks, however as Sly said;
Sly wrote:verify that you're same person with papers from city hall/mayor's office, old and new ID cards. You have to roleplay those stuffs and RP with LSPD about changing your legal name for proper reasons
If you don't want to go through all the trouble, simply wait the two weeks and re-apply again but with a new 'reason of request'.
-Pretty much answered. (PM if you need to)