He was the only remaining “true” heir of the House of Black. 12 Grimmauld Place was gifted to Harry Potter, Sirius’ godson. In which case, Harry or Draco Malfoy (related to the House of Black through his mother Narcissa) would’ve likely inherited the title of Head of House. Possibly even Andromeda Tonks or her grandson, Edward “Teddy” Remus Lupin.