It'd be difficult to directly measure "well known because of sports team", which I agree is a completely different question, but I think there are a few proxies

It'd be difficult to directly measure "well known because of sports team", which I agree is a completely different question, but I think there are a few proxies you could use to try to address the question. If you normalize whatever measure of sports team popularity by other measures of a city's prominence/global reach it might turn up something. Just thinking on the US scale if you took each team's popularity and divided it by the size of the associated city (population), the Green Bay Packers would probably come out on top of US pro sports, which seems accurate.