Noble, of noble birth
Aleece is a modern phonetic variant of Alice, which ultimately derives from the Germanic name Adalheidis. It carries the same etymological roots meaning nobility and high status, though it is used much less frequently than the traditional spelling.
Less common today
Aleece isn't in the latest US Top 1000. It last peaked at #4,141 in 1990.
US births per 5-year period, 1990βpresent (SSA data).