New Titles
There’s every likelihood that she would be buried at St. George’s Chapel, where her parents were interred. Her coronation day is probably to be proclaimed a national holiday, and her burial will be too.
Not Necessarily A Prince
It should be obvious that Charles would rule the country and make a declaration of remembrance when Queen Elizabeth dies. Then, he will settle on a moniker to represent his rule. There are a few possible answers to the question like George, Arthur, and Philip.