I am not aware of a similar word in English, but I believe the terms you are looking for are as follows:
Addition Property of Equality: If a, b, and c are numbers and a = b, then a + c = b + c.
Multiplication Property of Equality: If a, b, and c are numbers and a = b, then ac = bc.
A few technicalities aside, in general you can apply the same function f(x) to both sides of any equation: if a = b, then f(a) = f(b).
So maybe you are looking for Function Property of Equality. Unfortunately not one word. NOTE: https://en.wikipedia.org/wiki/Equality_(mathematics) refers to this as the Substitution Property of Equality.
By the way, you can square both sides of an equation while maintaining equality: if a = b, then a2 = b2.