I'm not sure there's been any spelling change, as "Paige" is as or more common as a spelling for the surname as "Page" is.
The regular use of Paige as a girls' name in the USA is one of the remaining mysteries to me. Paige first entered the SSA top 1000 list in 1952. There were two popular young women entertainers in the USA at that time with the surname (actress JanisPaige and singer PattiPage), but that may be a coincidence as this seems way before the era when a celebrity's surname would immediately become a given name for girls. So far I haven't been able to find an instance of a fictional character or well-known real life woman with the first name of Paige back in the 1940s or very early 1950s. I really think there must have been one. I suspect that rather than an entertainer this was a woman otherwise "in the news", as it's harder to find references to people who were briefly famous 60 years ago if they weren't entertainers.
It is rather amazing that some people think this is a "classic" name, as Paige basically became a female given name during the lifetime of persons still living today. To call Paige a "classic" name is to stretch the meaning of that term beyond reason, IMHO. :)