If a character mentions a person who is not a character in the play, is that name capitalized? For example:
JOHN. I have to give the apples to Jennifer.
Should Jennifer be capitalized even if she is not in the play?
Of course! All proper nouns are capitalized no matter where they are.
No, I mean are they fully capitalized? As in JENNIFER?
Some printers do; others don't. I don't know that there's a set rule.
In this case, the name "Jennifer" would not be capitalized. When a character mentions a person who is not a character in the play, the general rule is to treat it as an ordinary noun and follow the usual capitalization rules. Proper nouns, such as names of specific individuals, are typically capitalized, while common nouns, such as general objects or concepts, are not capitalized unless they are at the beginning of a sentence.
So, in your example, since Jennifer is not a character in the play but just a regular noun, it would not be capitalized:
JOHN. I have to give the apples to Jennifer.
If Jennifer were a character in the play, then her name would be capitalized:
JOHN. I have to give the apples to Jennifer.