The only time I believe surname comes into play is when operational upgrades are issued at the airport. These are done manually and the agent is presented with a list candidates. I don't know for sure, but it is possible this list is alphabetic. So if the agent just works from top down then surname does come into play. Of course the agent performing this task has other things to consider as well, such as the need to seat groups together, so they may be looking to free up specific seats rather than just move someone forward.
But I do not believe surname comes into play with regular computer-allocated seating assignments on domestic flights. I don't know what is used to determine seating priorities within a status level, but it could be things such as lifetime SC balance, date of ticket purchase, reverse numeric order of postcode, or age of your family dentist.