The Black Speech is the language J.R.R. Tolkien created for Sauron and Mordor in The Lord of the Rings.
Tolkien describes the Black Speech as having been devised by Sauron during the Second Age for the servants of his realm. Its most famous surviving example is the inscription on the One Ring: “Ash nazg durbatulûk,” part of the Ring-verse that expresses the Ring’s power over the others.
The Black Speech is not the same as Quenya or Sindarin, which are Elvish languages with much larger bodies of vocabulary and grammar in Tolkien’s writings. Nor is it Adûnaic, the language associated with Númenor. Tolkien supplied relatively little Black Speech compared with his Elvish languages, so modern reconstructions are limited.
The phrase “language of Mordor” can sometimes refer broadly to speech used in Mordor, but the named constructed language associated with Sauron is the Black Speech. That makes the answer more specific than Orcish, a broader descriptive term.