No one knows "A987" it has a clean slate with our user base. It's up to us to keep that name untarnished. Re branding has already enabled us to work with stakeholders without the negative feelings X123 brings, people get exited knowing there is a new project to replace it. Sometimes you're in a position to re-brand these legacy internal applications, but what if you can't? What if the name is set in stone but is a tarnished name? The best thing you can do is let the user base know there is a new sheriff in town and you want to work with them to address existing issues they have. Create a bug reporting link on your application, treat each customer complaint like a stage 1 missle alert. Give constant feedback to users on the status of their bug reports, make sure you track all changes and send out release notes to show progress. Make sure you show people the app is moving in the right direction. Everyone has a customer, even for internal applications your co-workers are your customer, make sure you treat them as such.
Remember you and your team control how you are viewed to the outside organization or world. Professional programmers value that reputation and want to see it stay solid. Scripters are there for a paycheck and aren't overly concerned with customer satisfaction. Be a pro.