What you mean by "denote" is not what is typically meant by "denote".
Common words are said to denote sets of individuals, e.g. "dog" denotes the set of all individual dogs in the given situation.
What you seem to be interested in is whether common nouns ever denote single individuals. The answer is that no, typically not. They do that sometimes when combined with determiners. "the" can be described as denoting a function which extracts the only element of a singleton set. So if e.g. "dog" denotes in the current context the set {Snowy}, then "the dog" denotes the dog Snowy.
Edit: An edge case may be nouns that can be used both as common and as proper nouns, such as "earth": "Earth is a beautiful planet" (referring to the individual by name) vs "We use resources equivalent to two earths" (using it as a countable noun). Though in that case one would probably say that these are actually two words with different grammatical and semantic properties, just like "run" exists as a noun and as a verb.