Jet (the database engine used by MS-Access) doesn't really support the idea of logins. There is a similar concept of the database "owner", but Jet only distinguishes between connections that use the owner password and ones that don't.
You could create an application login, and store that information in a table, but I'm not sure what good that would do you.
You might want to consider using MSDE. It is essentially a scaled down version of MS-SQL that is provided with MS-Access Professional, and is available for distribution as part of the MS-Access Developer Edition. MSDE supports the login concept nicely.