Max peaked in 2009 at rank 95 and now sits at 175. Over 165,000 American boys have carried the name as their full given name, not counting the considerably larger group of Maxwells, Maximilians, and Maxes who use it informally. The chart line is gentle, mostly because Max occupies the rare position of being both a full name and a nickname simultaneously.
The Latin Maximus root
Max derives from Latin Maximus, meaning "greatest," through medieval Latin Maximilianus and the German contracted form Max. The name has been used as a standalone given name in German and Central European traditions since at least the early 19th century. In English-speaking countries Max was historically a nickname before becoming a viable full name in the 20th century.
Notable bearers include physicist Max Planck (1858-1947), painter Max Ernst (1891-1976), and the fictional Mad Max film series starting in 1979. The Max Where the Wild Things Are connection (Maurice Sendak, 1963) gives the name a strong children's-literature anchor that has persisted for over sixty years.
The full-name versus nickname question
Max sits in an unusual category: parents who use Max as a full name on the birth certificate are making a different choice than parents who use Maxwell or Maximilian and nickname to Max. Both produce the same daily name, but the legal name carries different signals. The full-name Max parents are typically going for the German-Central European register or the short modern aesthetic. The Maxwell parents are leaving room for adult formality.
The cluster Max sits in includes Maxwell, Maximilian, and Maxim. Parents picking among these are often trading off between three considerations: how short do you want the legal name, how German-coded versus English-coded should it read, and whether the child should have a more formal option available later.
The counter-reading
The honest concern with Max as a full legal name is that it can read as informal in adult professional contexts. A 50-year-old executive named Max may have spent decades being asked whether the name is short for something. Parents who want the daily Max without the lifetime explanation often choose Maxwell instead. The three-letter boy names list places Max in context.