The Advanced Search Syntax allows "OR" operators using the pipe character | you just need to make sure you group everything together in parentheses so it evaluates the logic properly.

For example,

{[]:[Field1]="A"} & ({[]:[Field2]="1"} | {[]:[Field2]="2"})

evaluates as "Field1 is A and (Field2 is 1 or 2)"

Search Syntax (laserfiche.com)

However, because you need to process the results separately anyway, I'd say you're better off searching for each group individually, especially if you're expecting more than a few hundred results since looping through that many documents in one workflow instance can result in slower execution.

You could put all of your names into a multi-value token or a for each value activity, create a child workflow that actually does the processing so you get a fresh instance for each "batch", then pass the current value token as an input parameter to use inside of the search syntax.

{[]:[Field1]="A"} {[]:[Field2]="%(Input Value)"}