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).
Kate is now well below its former popularity. All-time it's been given to 86,076 U.S. babies, the 921st most common name by sound today, peaking at 2,550 in 2007, with 576 in 2025.
Kate has no common alternate spellings by sound.
Source: U.S. Social Security Administration, “National data” baby-names files (1880–2025).