What is the other name of Maxwell's right hand thumb rule?

Hint: The direction in which the right thumb points in a current-carrying conductor is considered as the direction of the electric current, and the direction in which the fingers wrap around the thumb is taken as the direction of the magnetic field.

Complete answer:
The other name of Maxwell's right-hand thumb rule is Maxwell's corkscrew rule.
In the direction of current, according to Maxwell's corkscrew, the direction in which we spin its handle is the direction of the magnetic field.
The direction of the magnetic field surrounding a straight-current carrying conductor is determined using this rule.
Maxwell's corkscrew rule is based on the movement of the corkscrew.
A fluctuating electric field generates a magnetic field, and a varying magnetic field generates an electric field, as is well known. The magnetic field lines and the electric current lines are perpendicular to each other.
Consider the use of a corkscrew to open a tightly sealed bottle. The corkscrew revolves in a clockwise direction as it travels inwards. The direction of the electric current is now assumed to be the direction of the corkscrew, and the direction of the magnetic field lines is assumed to be the direction of the handle.

Note:
The right-hand thumb rule, in which the direction in which the right thumb points is taken as the direction of the electric current in a current-carrying conductor and the direction in which the fingers curl around the thumb is taken as the direction of the magnetic field, is identical to Maxwell's corkscrew rule.