Arne Street was originally called Charles Street. Its name changed as part of the London Post Office rationalisation of street names in 1937 when those London thoroughfares with the same names were re-baptised with some loss to historical continuity and tradition.
The change of name to that of a Georgian composer reflected the Georgian origins of the street when first built. That is a forlorn memory as the dominant character is now 19th to 20th century, with no 18th-century survivals.