Step 1: Each ring is a quarter turn, so the facing direction repeats every 4 rings: Jayesh, Rajesh, Mahesh, Suresh, then back to Jayesh.
Step 2: Divide the total rings by the cycle length: \( 3926 \div 4 = 981 \) remainder \( 2 \).
Step 3: Only the remainder of 2 matters, starting again from Jayesh: ring 1 gives Rajesh, ring 2 gives Mahesh.
\[ \boxed{\text{Mahesh}} \]