not sure about 2013, but 2010 you can secure a db with a password - but this does not ask for a username.
if this is the case, go to File>Info and select 'Encrypt with Password' option to disable
Otherwise it sounds like your db has a routine for logging in users - this may be for security and/or tracking who does what, so disable at your risk. Since this is something that happens when you open the db, it will be triggered either by a macro called autoexec (in which case delete, rename or modify as required) or a setting in the db under File>Options>Current Database - Display Form - change to none in the dropdown.
Just another thought, and it's years since I've used it so can't remember the details but if this is an old db (.mdb) you may have implemented workgroup security - basically using a .mdw file. However I don't know how you would disable that, probably need to copy all objects to a new db. I'm sure there are responders here who still know how to do this