Yep, Amparo is right, Amparo Law is sometimes used.

Mi diccionario jurídico (Alcaraz Varó - Hughes) dice:
Amparo: protection, legal protection
amparo constitucional: constitutional protection
amparo de los tribunales: court protection
amparo jurídico: legal protection, equal protection of the law

Como han expresado los colegas, tal vez convenga dejarlo como Amparo Law con una nota explicativa del traductor ya que la traducción Protection Law resulta demasiado suelta a mi parecer. Saludos y suerte.

Juicio de Amparo = Court Injunction
A court order for the protection of one's civil rights

Asked many times, and usually answered the same ways ad nauseam.

Amparo sounds like a girl's name. Who goes to college to study a girl's name?

Courts engaged in judicial review of administrative action are increasingly using the term ‘rationality’ to describe at least some aspects of the standards ...

Sorry, Tom if it sounds like a girl's name. "Miranda" warnings also sound like a name, yet, the have no direct translation into s Spanish speaking document, as the case only applies to the United States.

Ana, for what it is worth, I will copy here what Thomas West says:

Amparo 1. (Mex) amparo [appeal for relief under the Constitution in a case of violation of civil rights. This is a constitutional remedy aimed at preserving the rights and freedoms established by the Federal Constitution from legislative acts, acts of authority and court decisions, as well as preserving local and federal sovereignty in interstate and federal-state disputes] 2.[Arg] amparo [Argentine amparo is a judicially created remedy whereas Mexican amparo is a constitutionally created remedy. Unlike Mexican amparo, Argentine amparo cannot be used as a substitute for habeas corpus or appeal, and whereas Mexican amparo can be used only to challenge state action, Argentine amparo will lie against actions of private groups such as unions.]

amparo administrativo (Mex) amparo proceeding against acts of administrative officials, when it is not possible to resort to an administrative tribunal.

note in Mexico...
The judicial action of Amparo has the objective of resolving disputes arising from the laws or acts of authority that violate the individual guarantees of the Constitution, the laws or acts of Federal authority that affect the sovereignty of the States, and the laws or acts of State authorities that invade the Federal sphere.