Hi Dilara,
there will be no problem to New USer Request Type. i see that your initial question was, user was able to change user name. Could you clarify, if it was id or name? Also, could you say, how did you stop users from doing that.
Since your user authentication data source is LDAP. there is no need of Sync job from LDAP. 2051 is a global setting, i.e for all users. So, there should not be any issue for some users.
Regards
plaban