Noble, of noble birth
Allesha is a modern phonetic variant of Alicia or Alice, which ultimately derives from the Germanic name Adalheidis. It carries the traditional meaning of nobility and high status, though this specific spelling is a contemporary American innovation.
Less common today
Allesha isn't in the latest US Top 1000. It last peaked at #6,211 in 1994.
US births per 5-year period, 1990βpresent (SSA data).