parenthesis, then address. After that is lists several first names in parenthesis. I'm guessing they are the children's names. Should I index them with the last name, or not index them at all.?
Give them each their own Entry with Ctrl+B i. e. <Blank> Surname.
From the Field Help for the Surname Fields:
“Do not assume a surname from the surnames of others mentioned in the document.”
The names in () are the spouses and you can index those names in the Spouse given name field, don't assume the last name so that is blank so do cont B or Command B to leave the word Blank in the field.
You're welcome, Beverly. I took from your question that you literally had a single record with a principal person and several names in parentheses, making them more likely to be children than a spouse. If there were just one name in parentheses then that is normally a spouse and is indexed in the Spouse's Fields as @scable2001 has said. I probably should have asked you to Share your Batch info so that I could have looked at it to be sure which situation you have.
We all should see the batch to answer a question about a batch. Always put the batch no. and example is
XXXX-XXX it is listed in [xxxx-xxx] at the end of the batch!