The generated Web Service reference class derives itself from SoapHttpClientProtocol, something like this:

[System.CodeDom.Compiler.GeneratedCodeAttribute("System.Web.Services", "4.0.30319.18408")]
[System.Diagnostics.DebuggerStepThroughAttribute()]
[System.ComponentModel.DesignerCategoryAttribute("code")]
[System.Web.Services.WebServiceBindingAttribute(Name="MyGeneratedWebServiceSoap", Namespace="http://www.killroy.com/webservices/")]
public partial class MyGeneratedWebService : System.Web.Services.Protocols.SoapHttpClientProtocol
{
    ...
}

SoapHttpClientProtocol has a read/write UserAgent property, so what you could do is derive from this class again and customize the user agent like this (this way you can automatically replace all instance creations of the original class by the new one):

public class SuperWs: MyGeneratedWebService
{
    public SuperWs()
    {
        UserAgent = "Mozilla/5.0 (Killroy was here)";
    }
}