Windows service - how to make name configurable

You can simply read it from the app.config and set it in the installer classes.
Normally, a class that inherits from Installer is automatically created. It contains a member of type System.ServiceProcess.ServiceInstaller, most likely named serviceProcessInstaller1. This has a property ServiceName you can set. Additionally, you need to set the ServiceName property of the ServiceBase derived class to the same value.
In a default implementation, these are set to constant values in the respective InitializeComponent methods, but there is no reason to stick with this. It can be done dynamically without problems.

I though I'd add my 2 cents since I ran into this. I have a file called "ProjectInstaller.cs" with designer and resources under it. Opening it up in design shows MyServiceInstaller and MyProjectInstaller as items on the design surface. I was able to change the names in the ProjectInstaller() constructor, and manually loaded the config file from the module directory:

public ProjectInstaller()
{
    InitializeComponent();

    var config = ConfigurationManager.OpenExeConfiguration(this.GetType().Assembly.Location);

    if (config.AppSettings.Settings["ServiceName"] != null)
    {
        this.MyServiceInstaller.ServiceName = config.AppSettings.Settings["ServiceName"].Value;
    }
    if (config.AppSettings.Settings["DisplayName"] != null)
    {
        this.MyServiceInstaller.DisplayName = config.AppSettings.Settings["DisplayName"].Value;
    }
}