AL-WAASI’ (ٱلْوَاسِعُ) is used to refer to God, so a person’s name should be Abdul Waasi (or with a different spelling Abdul Wasey).
Ideally other people should also use Abdul Waasi to refer to this person, however, if they don’t then there’s no sin in it. No one should, however, call or refer to the person as Al-Waasi since that is specific to God.
Personally, I believe that Waasi without the prefix of Abdul doesn’t make much sense as a name for a person. Abdul Waasi means the servant of the boundless or the servant of the all-encompassing. However, without the context of God it simply means wide or broad.