So, they're trying to change their 'title' to make is sound like they're more American--it's the Democrat party.
Other than it is the name used by Republicans to annoy them, what is your source for that being the official name of the party?
It would seem that "Democrat" is the noun for the party member, and "Democratic" is the adjective label used to name the party.
http://dnc.org/
Go ahead and keep annoying them, but don't mislead fellow conservatives about the matter. It risks making us look ignorant.