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).
Dax climbed for decades and has been a steadily popular name ever since. All-time it's been given to 11,934 U.S. babies, the 1,035th most common name by sound today, peaking at 749 in 2019, with 393 in 2025.
Dax has no common alternate spellings by sound.
Source: U.S. Social Security Administration, “National data” baby-names files (1880–2025).