Sounds like you need to sort your records differently and update the "sorted by" field designation in your sub summary layout part accordingly.
You might sort on a calculation field that lists the last name, First name in one field.
You might sort by the last name field and the first name field with the subsummary part specfiying the first name field as its "sorted by" field designation.
You might sort on an ID field such as a serial number instead of names since people can have the same first and last names. You can sort by last name and then list the ID field as an additional sort field and set your sub summary part's "sorted by" field to be the ID to get an alphabetical order but different sub summary parts even when the names are identical.
Are you able to sort by two different fields in one sub summary section? If so, how?
No but you don't need to. You can sort your found set by two different fields as described in my previous post. You then select the "more specific" field (the first name field) as the "sorted by" field for your sub summary layout part.