It just depends what you mean by "phrase". The everyday sense is an expression (constituent) containing several words, and since the name of an individual person or thing can perfectly well have several words, then yes. A proper noun can be a phrase, with several words. But in such a case, we would be more likely to refer to it as a "proper name" than a "proper noun", because using the word "noun" is often taken to imply that there is just a single word there.
In the grammarians' sense of "phrase", though, a phrase can have just a single word. The subject of a sentence, for instance, is a noun phrase, and of course a sentence subject may be single word. Here, the facts of language impose a certain interpretation for "phrase".
Another instance where the facts of language impose a sense that traditional grammar may find unintuitive is coordinate conjunction. A fundamental rule for how "and" works is that the grammatical category of a coordinate constituent is the same as the category of the two constituents that were conjoined. For instance, two verb phrases conjoined by "and" make up an expression which occurs in the same grammatical contexts as a single verb phrase. This rule works quite generally, and it tells us that the coordination of two nouns, common or proper, is a noun, even though it contains several words.