A section of Hull supporters unveiled a banner at the KC Stadium during Saturday's 1-0 home defeat to Crystal Palace in protest against owner Assem Allam that prompted stewards to intervene, sparking confrontational scenes.
Allam has turned around the club's fortunes since taking charge and laid the foundations for promotion to the Premier League, but his decision to carry on with plans to rebrand as Hull City Tigers from Hull City AFC has been met with continual vocal opposition.
Bruce, though, wants the Hull faithful to concentrate on getting behind the players on matchdays in order to help the team become established in the top flight.
Bruce said: "The one thing any club needs is stability at the top, which we have, but there's a situation that's arisen with the name change.
"What we all need to do is concentrate on what we are and where we are. I can understand supporters' frustrations, they have a right, but let's not make it a distraction. Let's not make it an excuse.
"Let's stay together and make sure we go forward together. As a football club we can do without the distractions. It's hard enough on a Saturday without all that.
"People are entitled to opinions, of course, I'd never suggest otherwise, but it's probably a wrong time to voice their opinions on a Saturday afternoon with a game going on."
