Fulbright and Jaworski become Jaworski and Fulbright. For many this would be a bother. But not all of us are there. Some would have great difficulty in giving up. Following Jesus often puts us in a position of downward mobility.
Upward mobility is a worldly value - downward mobility means following.
Philippians 2 shows us that way. I feel that in my own ministry. I never want you to pay much attention to Jim Singleton, I'm just a poor old sinner. My goal is to point you to Jesus Christ. If that means different ways of doing ministry here I would encourage that.