Hmm... strange - in my post, I see this line correctly, but in your reply project part is broken - maybe something with HTML escaping... anyway, the server_name line should look like this:
server_name ~^(www\.)?(?P<project>[^.]+).mydomain.com$;
server_name ~^(www\.)?(?P&lt;project&gt;[^.]+).mydomain.com$; (entitied version)

I'm basically cathing this variable in regexp while parsing server_name.

Greets