I believe that you have no need to worry about personality changes. My first boy, Max, has a very confident, strong personality. He was 1 year old when we brought his brother Teddy home.
I ended up with 2 very strong personalities, but they get along very well.
The only negative influence on each other is barking. They definitely compete with each other in that department.
It's not random, all day barking, thank goodness. Mostly in the car for fun, and a few triggers at home.