What is the name of this old 1940-1950's Pepsi Logo?
If you're referring to the font name, it's probably hand drawn. Notice that the bottom of LA are curved.
If you mean an unofficial name used by antique collectors for this version, you should post your question in a forum for Pepsi collectors.
Doesn't it feel like those letters were a forerunner to Herb Lubalin's Serif Gothic? Well, except for the swashy ones that is ;) The E,L and I are almost dead ringers...
It does look similar to that font.
Here's the progression of the logo up to that point.