it could be a couple of things.
1. If Charles follows tradition then he will take his fathers
family name, which is
"Schleswig-Holstein-Sonderburg-Glucksburg".
2. He might also take the name his father choose when he came to
England and that is "Mountbatten".
3. The other option is that he will brake tradition and choose
his mother house name of Windsor, which is not the original name
but was chosen by George V during world War I because
"Saxe-Coburg-Gotha" was not British enough.
Then again Charles or "King George VII" (as he said he will
probably be crowned) could just make up a new family name.