There are multiple origins and meanings for the name Dai:
1. Shortened form of the personal name David - "beloved"
2. Derived from the Arabic (داعي) [daee] - "propagandist; preacher calling to the true faith (Islam)". An epithet of Prophet Muhammad.
3. Japanese given name (大) meaning - "great, large"
4. Vietnamese name (Dài) meaning - "long; penis"
May also refer to Dai (feminine name).