NBA player Damian "Dame" Lillard is the influencer behind this unusual nickname. Dame made the charts for the first time in 2021, following Lillard's gold medal in the 2020 Summer Olympics.
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As a girl name, Dame references the English noble title, the female equivalent of a knight.

Crazy Nicknames for Boys

Nicknames for Boys

Dame

This noble title — the female equivalent of a knight — makes an inventive choice for a daughter. More subtle than Queen or Princess, Dame is a fresh way to get in on the regal word name trend. We know of at least one female Babyberry named Dame, although it's never been given to more than five baby girls in a single year.
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We've also seen Dame used as a nickname for boys, a la NBA player Damian "Dame" Lillard.

Dame

Dame Origin and Meaning