What is the name of this Peanuts character wearing a purple shirt and purple/pink shoes?
She is one of the twins from this scene:
From the Peanuts.com FAQs:
The twin sisters named “Three” and “Four,” who are most commonly recognized as the bouncy dancing girls in A Charlie Brown Christmas, were characters from the daily PEANUTS in the 60’s. They had an older brother named “Five.” In the strips’ story line, their father names them with numbers in protest of society’s ever-growing trend of reducing human lives to statistics. Their last name is actually 95742 – the family’s zip code.