Active Directory Domain Name for authentication

I have a bit of a code that takes an ldap string, a username, and a password, and then attempts to authenticate with the ldap server. The username may or may not contain the domain name, e.g., "DOMAIN\username" or "username" was valid input to this code.

From the ldap string, I will have a clear url, that may look like this LDAP://servername.com/DC=...etc. If I split out the server name portion, I get "servername.com", or "servername.corp", or whatnot. But if I attempt to login with servername.com\username, it does not authenticate. So one option is to split off the last ".", if there is one. Is this valid from an active directory perspective? What happens if there are subdomains such as xyx.servername.com?

I must admit I don't know enough about active directory to answer the above questions, and I can't find documentation that explains them. Some documentation that supports your answer would really help!