May Allah reward you with goodness. Is there anything (wrong) with being named (Awwab)?

It is permissible to be named "Awwab," provided it is not intended as self-praise. It means one who frequently returns to Allah, the Exalted, from his sin, and it resembles the name "Ayyub." As for names that imply self-praise, it is permissible to be named with them if they are merely used as a proper noun. However, if they are intended for showing off or if the meaning of self-praise is noticed in them, then they must be changed, just as the Prophet, peace and blessings be upon him, changed the name "Barrah."