Proper nouns can be homonyms, just like any other words.
But what is a homonym? According to Merriam-Webster, the primary meaning of homonym is a word that is spelled and pronounced like another word but is different in meaning; the term can also refer to the related concepts of homophones (words that sound the same but differ in meaning or spelling) or homographs (words that are spelled the same but differ in pronunciation or meaning).
Clearly, this definition of homonym can be applied to proper nouns. Because proper nouns (including personal names like Cole and place names like London) are still real words, they may also be homonyms. For instance, this article lists Greece and grease as homonyms, even though Greece is most certainly a proper noun. (NB: the definition of homonym does not require a specific part of speech, but merely requires a word.)