The Toronto Blue Jays' founding ownership group was headed by the Labatt brewery, whose marquee Ontario brand was (and still is) Labatt's Blue Pilsner. Pouring, both from this fact and the from longstanding Toronto sports tradition of sports teams wearing blue (NHL Maple Leafs, IL Maple Leafs, CFL Argonauts, University of Toronto Varsity Blues), Labatt decreed that the name must incorporate the name of the colour. Rumour has it that the "Toronto Blues" was the initial frontrunner before beng displaced by rather harmless migratory birds. Why Blue Jays? I can't really say other than to note that Blue Jays do inhabit the "true north strong and free" and fit in with the Baseball tradition of naming teams after nonthreatening birds (Orioles, Cardinals).
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The Blue Jays name came from a "Name the Team" contest held when the franchise was born. Several people suggested the name Blue Jays, and a draw was held to pick the actual winner. The information can be found in the Blue Jays Media Guide (which I have read before, but don't have with me right now).