The Daemon Prince has Immortal Champion where your declare its dedicated to a chaos god, but does it get that keyword for allegiance abilities? Seems odd that it wouldn't. And if it doesn't then couldn't I choose a different dedicated god than the one I'm playing with?
For Example I'm a Slaanesh player. I want to take the the daemon prince as an ally but can I dedicate it to one of the other gods of chaos, if it doesn't even receive the keyword of the god it's dedicated to. Seems strange to me.