Noble or of noble birth
Allyzon is a modern creative spelling of Allison. It ultimately derives from the Germanic name Adalheidis, which is composed of the elements 'adal' meaning noble and 'heid' meaning kind or type.
Less common today
Allyzon isn't in the latest US Top 1000. It last peaked at #10,375 in 2012.
US births per 5-year period, 1990βpresent (SSA data).