An heiress; a person who inherits property or rank
Aeiress is a modern phonetic spelling of the English word 'heiress'. It represents a contemporary trend of adapting occupational or status-based nouns into unique personal names by altering the spelling to appear more decorative.
Less common today
Aeiress isn't in the latest US Top 1000. It last peaked at #10,447 in 2019.
US births per 5-year period, 1990βpresent (SSA data).