What is the basis for the changes to the Aircraft Overview Notes that make reference to the model designation UH-1 rather than AH-1?

"Mating the proven transmission, the "540" rotor system of the UH-1C augmented by a Stability Control Augmentation System (SCAS), and the T53 turboshaft engine of the UH-1 with the design philosophy of the Sioux Scout, Bell produced the Model 209". Could this be the reason for the use of UH-1?

This is more a statement of the design origin or heritage rather than a direct justification for the use of the UH-1 designation. I think we should stick to the AH-1 designation as this is what the aircraft is called on the Bell history site (1965)

I agree. While the 209 may have been referred to at some point with the UH designation, I don't think it was ever official.

As an interesting side note (also from Wikipedia):

"By June 1967, the first AH-1G HueyCobras had been delivered. Originally designated as UH-1H, the "A" for attack designation was soon adopted and when the improved UH-1D became the UH-1H, the HueyCobra became the AH-1G. The AH-1 was initially considered a variant of the H-1 line, resulting in the G series letter."

Which explains why the first production version started with "G" instead of "A" -- but don't ask why the LAST production version was the F! Maybe it's like when Dad saw Junior's report card: "What does F stand for? Finished?"

Mike Verier in "Bell AH-1 Cobra" (Osprey, 1990, pp 30-31) notes that due to various short timeframes, proposal and marketing needs, and so on, Bell referred to what would become the 209 as a "modified UH-1H" in order to calm US Army doubts about how quickly they could produce it. In the language of the proposals, it was called the UH-1 Cobra. General Howze is the one who gave it the nickname of HueyCobra.

The Army wished to stay with the UH-1 procurement system, though, and the order for the first two production aircraft designated UH-1H. But just a few days later, it was changed to AH-1G (with G being the next available "open" letter in the UH-1 family). The Army at that time was having legal issues with Piper Aircraft, who also named aircraft after Indian tribes, so the Army went with "Cobra" rather than the tradition of helicopters also being named after Indian tribes. And it's been that way ever since!

So 209 by itself, or used in conjunction with AH-1, seems perfectly accurate.