Anyone from the Village, Hillside, Wimbledon Park or the Trinity/Dundonald areas would laugh at you if you claimed you lived in Wimbledon if you lived there. It's South Wimbledon. I'd say anything south and east of the Esso garage on Merton Road is South Wimbledon. Estate agents would market it as Wimbledon - Ryanair would say it was Wimbledon Central 😄 but people who know the borough know that it's not really what you'd call Wimbledon. When people think of Wimbledon, they think of houses like this
https://www.zoopla.co.uk/for-sale/details/65975464/
Saying it's Wimbledon would be acceptable if you were on holiday and people asked where you came from - it's the greater area that people know from the tennis, but South Wimbledon is South Wimbledon, and Merton Park (which tbh has a greater claim to be the South part of Wimbledon, with it being directly south of the town centre) is Merton Park.