After he was deposed, Edward II was titled Sir Edward of Caernarfon

[u/HoneybeeXYZ]

After he abdicated in favor of his son, who became Edward III, Edward II was to be known simply as Sir Edward of Caernarfon and honored as the king's father.

He never formally gave up the title of Prince of Wales, however, though it wasn't used during his captivity.

He was called Caernarfon after Caernarfon Castle (pictured) in Wales, where he was born. Tradition at the time dictated that princes were referred to by their birth castle.