Solid line = floor (spellings that unambiguously belong to the group). Shaded band up to the dashed edge = ceiling (the most it could reach if every ambiguous spelling counted here).
Max is now well below its former popularity. All-time it's been given to 172,766 U.S. babies, the 333rd most common name by sound today, peaking at 4,184 in 2009, with 2,164 in 2025.
By sound, Max also includes the spellings Maxx.
Source: U.S. Social Security Administration, “National data” baby-names files (1880–2025).