The name Hannah appears in the Latin Bible as Anna. Strong's Concordance translates the name as "grace."
If you're wanting Latin for "gift of God," it's usually donum Dei, but you might prefer gratia Dei - "grace of God" but translated "gift of God" in Romans 6:23 and 2 Titus 1:6.
Your friend might not like either Anna, donum Dei or Anna, gratia Dei., saying her name is Hannah, not Anna.
I suppose you could substitute Hannah, donum Dei or Hannah, gratia Dei.