Name for the piece of material located, usually, inside the collar of a jacket or coat which allows garment to be hung from a hook
Solution 1:
That is called a hanging loop or a locker loop as pointed out by @ColleenV in the comments above.
Hanging loop
- A cloth strip at the collar of a coat, jacket; on a tea towel, an umbrella etc
[Wiktionary]
Locker loop
- (clothing) A small band at the back of the shirt, by which it can be hung up.
[Wiktionary]