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).
Louis has been climbing in recent years. All-time it's been given to 409,317 U.S. babies, the 492nd most common name by sound today, peaking at 7,296 in 1921, with 1,397 in 2025.
Louis has no common alternate spellings by sound.
Source: U.S. Social Security Administration, “National data” baby-names files (1880–2025).