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.