Theory:

Characters:

Sherlock Holmes - the famous detective

Doctor Watson - a doctor and Sherlock’s friend

Jabez Wilson - a red-haired shopkeeper

Vincent Spaulding - Wilson’s assistant, also known as John Clay

Duncan Ross - Spaulding’s accomplice, a man with red hair

Mr.Jones - a detective from Scotland Yard
Explanation:
 
Sherlock Holmes is a very famous private detective and the main character of the story. He was smart and intelligent. Till the end of the story, we can never find out his plans for solving the case.
 
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Dr. John Watson is Sherlock Holmes’s partner. He is a doctor by profession and Sherlock Holmes friend.

Jabez Wilson was a red-haired pawnbroker. He works for Red-Headed League for a few weeks.

John Clay/Vincent Spaulding is a criminal working at Jabez Wilson’s pawnshop under the anonym Vincent Spaulding. He was Wilson's assistant, also known as John Clay.

Archie/Duncan Ross/William Morris was also a man with red hair. He is
John Clay’s associate and is the head of the League.
  
Peter Jones is a Scotland Yard detective.
Reference:
State Council of Educational Research and Training (2019). Term-1 English Standard-7. The Red-Headed League by Sir Arthur Conan Doyle (pp. 45-49). Published by the Tamil Nadu Textbook and Educational Services Corporation.