Virginia's name is randomized when La Fiesta Tech is generated. The name "Virginia Allen" is only referenced in the game files.
While the style of hat she wears is available to teens and older, the color is not available to young adults. If she is given a makeover and the hat is removed, it can't be recovered until she becomes an adult. If certain expansion packs are installed, the color is also unavailable to adults and cannot be recovered until she becomes an elder.