I am a Mustang guy, and I'm telling you the first training units were told their plane was the "P-51 Apache," and likewise the ground attack guys (where the "A" comes from) were training in "A-36 Mustangs." The very first North American wartime poster for either airplane named it "P-51 Apache," which was the project name from the very beginning.
A-36 Mustang
P-51 Apache
I have seen the wartime poster for the original "P-51 Apache" and I am still looking for it online.
See "Kinzey, Bert. P-51 Mustang in Detail & Scale: Part 1; Prototype through P-51C. Carrollton, Texas: Detail & Scale Inc., 1996. ISBN 1-888974-02-8"