I don't think it would be a good idea for Charles to change the title of the monarch but rather he should focus on living a life that aligns with being "defender of the faiths". Actions not words. Respect the history of his title and at the same time the multinationality and religious diversity of modern Britain (and his other realms).
He may have enough trouble on his hands with the "Queen Camilla" thing without rocking the boat on how the monarch is styled.
When was the last time the sovereign decided to change their title without the direction and advice of their ministers?
The actual title the Queen holds is 'Defender of The Faith' - singular as it is the Anglican faith.
The monarch can't change the title as the title was bestowed by parliament so only parliament can change it and Charles, himself, has backtracked from his desire to be 'Defender of Faith' since he made that comment in the early 90s.
The monarchs of the 16th Century had no trouble changing the title, or causing it to be changed, to suit their personal interests. Henry was given the title in 1521 by Pope Leo because of the book he wrote defending aspects of the Catholic faith, including papal supremacy, against Martin Luther. But as more time passed without his wife producing a son, and his eye increasingly and more intently wandered, he set out devising ways of getting around the problem so he could marry another woman. In 1533 he persuaded Parliament to pass the Act of Succession rendering his daughter, Mary, illegitimate and legitimising his second marriage, and then the Acts of Supremacy in 1534 making himself the head of the Church of England and then in 1544 he got Parliament to make him Defender of the Faith, the faith now being that of the C of E. But then he died and his daughter Mary ended up queen and she set about "righting" her father's wrongs and slaughtering people who disagreed with her religion and got Parliament to repeal the legislation which made the monarch the head of the C of E and defender of that faith, and it wasn't till after the Restoration of the monarchy that the title came back and as meaning defender of the C of E faith.
Seen in historical context, Defender of the Faith is a relatively modern and fluid concept which has changed with the times and with the whim of the monarch of the day. I see no reason whatsoever why it should not change again in this increasingly secular 21st Century Britain to reflect the multi-faith nature of modern British society, especially in the state of flux that will inevitably follow the death of the woman who has been queen longer than most of her subjects have been alive.