The 440 was introduced in C-bodies in 1966. There were 2 versions; 350 hp. with single exhaust, Imperials, New Yorkers. Optional 365 hp., with dual exhaust and better camshaft, like the one used with 383 4-barrel. These engines still had smaller exhaust valves, like a 383.
The 350 hp. 440 was carried over for 1967 C-bodies. In 1967, the 365 hp. 440 was updated to 375 hp. with better heads with larger exhaust valves and larger ports. Also, these engines had larger 750 cfm. Carter AFB., and camshaft with more lift and duration. The engines were now called "TNT", "Magnum", or "Super Commando" depending on vehicle application. This 375 hp. 440 was optional on C-bodies, and newly available as the standard engine in R/T and GTX.
Chrysler had a habit of badging only optional engines when installed in vehicles. This is why R/T and GTX had no 440 fender badges, since this was the standard engine in them. When equipped with an optional 426 Hemi the fenders got badging announcing this. Since the 440 Magnum was an option on a 1967 Charger, it got the 440 Magnum sign. Both versions of the 440 were optional on C-body Dodges, but I think they only came with 440 4- Barrel sign.