You probably have Client for Microsoft Networks and/or Microsoft Family Logon installed clients under your network properties (accessible by right clicking on Network Neighborhood and clicking on properties). If you don't need either of these, just simply remove both of them and click OK. It may (mine always does at least) pop up with something like "the network is not complete, continue?" to which just click yes.
I don't know if you specifically need either of these, depending on what you are doing you might only need IPX protocol and/or TCP/IP. If you're doing, say mapping drives to another machine to transfer files, then I believe you do need Client for Microsoft Networking installed (as well as IPX) at least.
If you don't have any networking installed, and are just getting a straight up Windows Logon (not network) box, check out this link:
http://www.starpower.net/support/pc/...on.screen.html . It's for Windows 98, but I don't see any reason why it shouldn't work for WinME.