This address is close to Lisburn Road. It is not to be confused with an earlier Marlborough Court in the city centre.
Marlborough is an historic market town in Wiltshire. It appears in the peerage title of the Dukes of Marlborough. However, given that there is a theme in South Belfast of royalty and royal residences (Adelaide, Windsor, Osborne, etc.), it seems most likely that this street is named after Marlborough House in London. It was built in 1711 for Sarah Churchill, Duchess of Marlborough. It served as the London residence of the Dukes of Marlborough. It then became a royal residence throughout the 19th century and first half of the 20th century (including the time when Marlborough Park etc. were named in Belfast). Since 1965 it has been the headquarters of the Commonwealth.
Marlborough Court was earlier an address off the east side of Princes Street between Marlborough Street and Queens Square, the name of which was approved in 1896.