I still prefer the Senators name since Ottawa is the capital but it is definitely weirdly used in their scheme. They have a helmeted Roman officer on their primary crest but being an officer in the Roman Army didn't mean you were a Senator. To be a Senator was to be a member of a specific sub set of the Roman Aristocracy which gave the holder the right to a seat in the Senate House to debate legislation and select the magistrates. Senators were selected for top military and government positions like Consul and Praetor but being a Senator didn't make someone a soldier. A Centurion, however, was always a soldier, the officer in charge of a Century of roughly 80 legionaries. So a guy in a helmet was more likely to be a Centurion than a Senator.
What I would really like would be for the Senators to come up with a logo similar to this one from the Twins:
Ottawa is also a city divided by a River, but its further divided between Ontario and Quebec so it would be really cool to have that emphasized. Perhaps by using two guys in red-lined togas on hockey skates shaking hands.