When is the user presented with this login window? Are they already logged on to the network or are they attempting to log onto the workstation? Are you trying to set this up on a single computer where all users use the same workstation or is the database intended to be multi-user on the network?
The network login has nothing to do with MS Access except for directory and file access permissions. So, before MS Access user-level security can come into play, one must negotiate the network login. This part of the security scheme is the most critical globally in that permissions here determine what users can do or see on the entire network, not just your Access database. This is the part I don't think you have authority alter.
But, let's say for the moment that the user is logged on to the network and has read/write & delete permissions for the directory where the database resides. Now you can begin to apply MS Access user-level security. Now you can use a generic username in Access user-level security and limit that user's permissions. You can, also, have a user called Dispatcher and give that user elevated permissions. And the same goes for a user named Administrator. However, I highly recommend administrators and dispatchers NOT be generic and you control their permissions through group permissions instead. I'm assuming the administrators and dispatchers are probably not high turnover individuals.
Your statement confuses me somewhat.
My problem is that when I set up the user level security it does not give a drop down menu to pick a name from
Are you looking at the Access login prompt and expecting a dropdown list like one sees with Windows? Access does not do that. You either know a valid MS Access username and password or you don't. In your case, that could be a genric userID if you want and doesn't even have to have a password - if you want. But, it would still require the user to log onto the network before logging onto Access - or be already logged onto the network through some other user's name (not a particularly good idea).
If you or someone involved were a programmer, it could be possible to not have user-level security and then through coding, use network login ID's to determine permissions for access to certain forms, etc. based on the user's network ID. This, however, gets very complex and assumes some measure of administrative rights to the network. I get the impression this is not one of your options.