If the fans gave a damn about the name in the first place, they wouldn't have let the team die in the first place. The team also wouldn't have thrown away the name in favour of Senators back in the 1920s.
They had their chance. They don't respect the name or the history.
I still refuse to blame the Ottawa fans for the team folding. They gave their fans a 25 year performance that made the Green Riders from the same era look like the 77-82 Eskimos; the ownership of Horn Chen and two doses of the Gliebermans. Nobody should be forced to endure that sort of thing for 10 years much less a generation.
As for the name change in the 1920s it was more the norm in that era, if not popular, to see teams of different sports within the same city adopt the same nickname. Perhaps the brief name change by the Rough Riders/Senators had more to do with that practice.
Ottawa had the NHL Senators and CRU Senators
Hamilton had the NHL Tigers from 1925-30 as well as the CRU Tigers. The Calgary team of that era was also known as the Tigers.
Pittsburgh's teams in MLB, NHL (1925-30) and NFL (1933-40) were all named the Pirates.
Brooklyn had the MLB Dodgers from the turn of the century until moving to LA. For 14 years from 1930 to 1943 they also had the NFL Dodgers. Across the river the New York football Giants came into existence in 1925 some 42 years into the MLB Giants' history. For 32 years the football and baseball Giants would co-exist playing mostly in the same Polo Grounds Stadium.