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 has been slowly declining from its former popularity. All-time it's been given to 172,766 U.S. babies, the 339th 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.