I think
Zeke needs
Ezekiel to back it up.
Zeke sounds very incomplete to me as a full name. As a nickname, I love it! I think
Ezekiel just looks much nicer on a resume than just
Zeke.
I know a little boy named
Ezekiel who goes by
Zeke 100% of the time. I have never heard anyone, including his parents, call him
Ezekiel, so maybe if you really love
Zeke you could call him that all the time, and have
Ezekiel on the documents and such.