Since you’re looking for correctness,
login, logout, logon, and logoff are all nouns:
"Please enter your login credentials."
"I see three logons but only two logoffs from this user."
The corresponding verbs are each two words:
"Please log in to see your reputation."
"You must log off and talk to a human."
Update: according to dictionary.com, the various definitions of login are all nouns and involve gaining access to a computer or computer service. Interestingly, logon redirects to login as an exact equivalent. Have the definitions evolved?