Do you place commas around a name?
My cousin John will visit me next week. My aunt Betty Jo will be my mentor.
Both of these examples involve one of the most complicated comma uses: the appendage comma with nonrestrictives.
Short answer: If you have only one cousin (or only one aunt), put commas around that person’s name. If, however, you have more than one cousin (or more than one aunt), do not use commas around the name.
Long answer: Let’s consider the first example: “My cousin John will visit me next week.” If you have only one cousin, then referring to your “cousin” is sufficient information to establish who you’re talking about. “My cousin will visit me next week.” As long as you only have one cousin, there’s no possibility of confusion in that sentence. So adding your cousin’s name is only extra information—good to know but unnecessary to identify him. In this case, “John” would only be extra information about that cousin already identified. Extra information such as this is called nonrestrictive information and is separated from the rest of the sentence with a set of appendage commas: “My cousin, John, will visit me next week.”
But if you have several cousins, referring to your “cousin” without a name would leave the reader confused as to who exactly you mean. So because you have several cousins, including the name “John” is suddenly necessary to identify precisely who you mean. In this situation of multiple cousins, “John” is restrictive information, and restrictive information doesn’t use the comma: “My cousin John will visit me next week.”
Now let’s look at the second example: “My aunt Betty Jo will be my mentor.” The same rules above about multiple cousins apply here: if you have multiple aunts, the reader will need a proper name to know which aunt you’re talking about. So if you have multiple aunts, “Betty Jo” is restrictive (no commas), but having only one aunt would make “Betty Jo” nonrestrictive (use commas).
For more help with nonrestrictive, study this page: The appendage comma with nonrestrictives.