Starry wrote:

Thanks for the effort but unfortunately the part that tends to be overlooked when I ask is that I'm referring specifically to this part

Nobody has yet to determine exactly what Paul did here, but it's in pictures for years so it held up well. It is the same strap used in the Help! film, as shown here, though

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Hi Starry,

It's called a "Dog Clip".  This site has more information (Posted here for guitar research only).

http://www.voxshowroom.com/northcoast/hofner/hofner_parts/hofner_strap.html

[This is an ] accurate reproduction of the strap originally used by Paul McCartney on his Hofner Violin Bass with the Beatles. This is an important detail to making your Beatle bass rig correct.

The strap is made of dark, chocolate brown leather, and includes a "dog clip" on one end of the strap (as Paul's did). One may either clip this dog clip to the tailpiece of the guitar, or to a short leather straplet (included) that replaces your strap button near the bridge. The straplet has a metal "D" ring to accept the dog clip.

Use this with any German made Hofner Beatle bass or the Hofner Contemporary Series Beatle Bass. This strap does not work with the Hofner Icon or Ignition Series basses due to the way the neck attaches to the body.