One way would be to change the Register SkinObject in the core, or create your own modified one.

I may be able to come up with a couple lines of code that you can place in your skin to accomplish this though.

Let me see what I can come up with.

Ok,  try this. In your skin find the User skin object (not the "register" skin object like I said earlier).

In an HTML skin it will be a token that says [USER], in an ASCX skin it will be code that looks like <dnn:USER runat="server" id="dnnUSER" />

Replace that with the code below:

<a class="SkinObject" href='<%= DotNetNuke.Common.Globals.NavigateUrl("Register")%>'>
                <%=IIf(Request.IsAuthenticated,HttpContext.Current.User.Identity.Name,"Register")%></a>