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).
Hayes has been climbing in recent years. All-time it's been given to 21,886 U.S. babies, the 374th most common name by sound today, peaking at 2,327 in 2025, with 2,327 in 2025.
Hayes has no common alternate spellings by sound.
Source: U.S. Social Security Administration, “National data” baby-names files (1880–2025).