There's a couple of things you can do. I know in some instances it is not possible to get rid of the box (to my knowledge).
The first one is to change your network settings. Right click on "Network Neighborhood" and you should see a list of protocols etc.. Double click on "Client for Microsoft Networks" and it will give you some options you can configure. Somewhere, there should be an option for "quick logon". Check this and OK. You will probably be asked for your Windows 98 CD and to restart your computer. On next reboot, it should work....
If not...
I've used this trick in Windows Me, so it may work in Windows 98 as well. It involves changing / adding some regisry stuff.
Start / Run / regedit [ok]
Browse HKEY_LOCAL_MACHINE. Now, my memory is cloudy, but I think the appropriate keys are Software / Microsoft / Windows / CurrentVersion / Winlogon
You will need to make the following data (string) by right clicking on the right window pane in Winlogon and choose "New" and "String Value".
The first string you should make AutoAdminLogon. Once you make it, double click on it and change the value to 1
The second one you should make is DefaultPassword. Leave this entry blank if you do not have a password. If you do have a password, double click on it and change the value to your password.
The last one is DefaultUsername. This will be the name you use to logon.
Once finished, close the Window and restart Windows 98. You should not see the logon box. If you still do, I'm unsure how to get rid of it. Maybe someone else will have better ideas.