Other thought for dealing with gate agent is if you pull the trip up on your app it shows your trip then the companion's trip right below your trip...

But again I am against doing things that hold up boarding. This is the type of thing that causes flights to delay. This is extremely inconsiderate for other passengers who may have tight connections since Southwest does things like sells flights connecting through DEN with a 45 minute connection.

The only solution is to contact customer service for the exact policy. None of us know. Get it in writing and keep it with you.