With Mulcair at the NDP helm and Rae leading the Liberals would there be a merger? Mulcair denies it but both have mused about "uniting progressives" and so has Jean Chretien. With a former provincial Liberal heading the NDP and a former provincial Dipper running the Liberals I'm guessing the idea would get serious consideration. But we'll just have to wait and see.
If it happened the new, merged party would need a new name. I'm betting it would be the "Liberal Democratic Party". Both get to keep their names, the oldest party's name comes first, "NDP" is promoted two letters in the alphabet and finally gets rid of the worn out "New". You heard it here first.