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Almost definitely, her body would be laid to rest at St. George’s Chapel, where her parents were laid to rest years before she was born. On the day of her coronation and the day of her burial, it is almost guaranteed that a national holiday will be declared in her honor.
Not Necessarily A Prince
Following the death of Queen Elizabeth, it should go without saying that Prince Charles will reign over the country and give a national declaration of remembrance for the occasion. His moniker, which will be used as a sign of his reign, will be chosen after that. There are several viable solutions to this question, including names such as George, Arthur, and Philip, amongst other possibilities.