In 2002 the Isle of Man’s Tynwald gave Land Of Our Birth official status as the island’s national anthem. The story was largely ignored by the UK media but Glasgow’s Daily Record felt the story deserved two lines, a month after the event:
The Isle of Man has replaced God Save The Queen with its own anthem, Land Of Our Birth. But they will still play the national anthem whenever the monarch visits.
Yes, it’s really that easy. God Save the Queen has no official status, so if you don’t like it change it. The Australians did so in 1974, on the basis of a public opinion poll (Encyclopedia of Australia):
In April 1974 the Whitlam Labor Government announced that, as a result of a public opinion poll, the Australian national anthem would be changed from God Save the Queen to Advance Australia Fair. God Save the Queen had been the official anthem since Federation in 1901. God Save the Queen would still be used on certain occasions to honour the Queen. The new anthem was considered more appropriate as Australia’s ties with Britain weakened. A suggestion to make Waltzing Matilda the national anthem was rejected, although Waltzing Matilda is recognised as a symbol of Australia and is often regarded as an unofficial anthem.