A little more on road signage - in the US they use control cities and/or actual information.
So on northbound Deerfoot up until Memorial, the signs would just say "City Centre". Beyond Memorial, they would say Edmonton... or maybe "YYC Airport" until Airport Trail then Edmonton beyond that. Southbound signs after Memorial would say Lethbridge. No sign would say "Deerfoot Trail", as that is useless information. This method of signage also applies to ring roads, like in Cincinnati where their
ring road carries an official name but nobody calls it that and no overhead signage says it. If we signed Stoney like that, no sign would say "Stoney Trail" but rather some combination of Banff, Edmonton, Lethbridge and Medicine Hat depending on quadrant and direction.
In theory, with no signs saying "Deerfoot", it's unlikely it'd have become the colloquial name. But then again, the
story of how Deerfoot got its name is pretty cool. So maybe it's good we needlessly flex it on every road sign instead of providing information to drivers.