At the login screen, how do I login to a domain account?
For example, on Windows the username might be something like email@example.com, where the domain is contoso.local.
Edit: The AD username happens to be the same as a local username.
You need to set up Network Account Server settings in Preferences > Users & Groups > Login Options.
In the company I work for I can either use DOMAIN\username or username@DOMAIN when logging in to the AD on from a Windows Machine, but on the Mac this is not required. I just type in username and my AD password, and it logs me in.
I've been having the same issue today and I believe I've resolved this (Yosemite).
I've got my local user (user.name) and my domain user (domain.local\user.name). I've added to OD auth correctly without issue.
When I attempt to log in with my domain user (domain.local\user.name) it rejects me for an invalid password. I tried out the password for my local user, and it worked, but threw an error when loading the desktop.
I've right clicked on the user under "Users & Groups" and gone into "Advanced Options" (which I found completely by accident). I then modified my "Full Name" - which was user.name - to be user.name.local.
After rebooting the machine, all worked and I could log into the domain user with the correct password without issue.
One thing to note here is that I didn't have to change the "Username" in advanced options here. There may be ramifications to this - see this Apple support KB for more information.
You can control this by setting the search order for each domain in the forest. This can by found on the Mac by going to: System Prefs->Users & Groups->Login Options->Click Edit next to Network Account Server Then Open Directory Utility and Click on Search Policy
mwidman has given you the answer for this.
If you wish to log in to your Active Directory domain account rather than the local account then precede the account name with the AD domain name and a .
So in your case contoso.local\louis
This assumes that you have already bound the Mac to Active Directory. I am also wary of using Spider-moe's solution - as a sysadmin I never like altering the search policy order.