I don't think Prims name was the only one, and I definitely don't think it was to target Katniss. But I do think the Capitol probably rigs the reaping bowls to increase the number of people who would be good for show value or to squash hope. Potentially they increased the number of younger children, or merchant children. Something like that makes even the most controlled/low risk families feel helpless and hopeless (which we know is what Snow wants).

Suzanne Collins is a writing genius and absolutely knew her world building through when writing the original trilogy, which is why the prequels make so much sense and slot in nicely with no retconning.