Likely adapted from a surname of Middle Eastern use, probably tied to a family or status term rather than a standard given name meaning.
Agassi is likely a surname-derived name with Arabic connections, and its exact meaning seems tied more to family, status, or lineage than to a standard given-name root. That kind of origin often gives a name a strong social texture: less about symbolic translation and more about identity carried through a family line.
As a given name, Agassi feels unusual and polished, with the sort of clipped, stylish sound that can easily move between surname and first-name territory. It has a cosmopolitan quality, partly because it is rare and partly because it does not immediately announce a single familiar tradition. Names like Agassi often gain their personality from usage rather than history alone, and that makes this one feel modern in the truest sense.