In the linguistic field of generative syntax, which is where this idea of "noun phrases" is treated scientifically, there is nothing preventing a noun phrase from only containing a single noun, just as there is nothing preventing a verb phrase from only containing a single verb, and so on. In fact, the noun is the only required element of a noun phrase in the modern formulation of generative syntax.
In common (non-scientific) usage, "phrase" is understood to be a unit larger than a word itselfbut smaller than a sentence, and does not necessarily correlate to the linguistic understanding of a "phrase". By this definition, a single word could clearly not be considered a phrase.
At the end of the day, context matters. If you're talking about the syntactic components of a sentence, as in "Saad is now a grown man" is composed of the noun phrase "Saad" and the verb phrase "is now a grown man", then it is absolutely correct to call "Saad" a phrase. But if you are just talking to someone, and you misheard them and you say "Can you please repeat that phrase?" you would not be expecting to hear a single word, and if someone says something you really like and you go "Wow, that was a beautiful phrase at the end there," they would understand you to be referring to a group of multiple words.