Windows Server 2012 R2 Active Directory Name

I need to setup a new Windows 2012 R2 server for a client.  This server will also serve and a AD DC.  I want to set the AD Domain name the same as the public website this company owns _ _ _ _ _ _ _ _funeralservice.com (27 characters including .com).  This company does not own another public domain name.  I know that the NETBION name allows up to 15 characters, and I would like it to match the domain name.  What are my options if any?

So if I name the Domain name the same as the public domain name ( _ _ _ _ _ _ _ _funeralservice.com), then the user login will be _ _ _ _ _ _ _ _funeral\User1.  I mean this will all work, but its a bit awkward that they do not match.  I was just thinking of going with the  .local route, but all the articles I have found suggest not doing so.  What would be the best resolution?  I do not believe the client is willing to purchase another shorter public domain.  

Also, should the domain include a subdomain such as internal. _ _ _ _ _ _ _ _funeralservice.com, or LAN. _ _ _ _ _ _ _ _funeralservice.com?  I have heard references there is a need to create a subdomain for the the AD domain name to avoid future conflicts.  I am not sure about the need to do all of that though.  I do not want to complicate things for a very small office network with one or two servers with less than 10 employees.  What's your take on all of this?