Qual é o nome da língua que os Orcs falam?

Uma de suas línguas é (rufar de tambores ...) orkish

Orkish was a general term for the jumble of languages used by the Orcs, composed from corrupted borrowings from other languages of Middle-earth. The variations in Orkish between different tribes and types of Orc were so great that it was often useless for communication, and so a standard language was necessary. Sauron devised his Black Speech for this purpose in Mordor, but in practice the Common Tongue was more normally used.

Como você vê, eles também falaram a Fala Negra , que era a língua entre todos os servos de Mordor, incluindo orcs. Foi criado por Sauron para fazer os orcs e o resto de seus servos se entenderem. Quando Sauron foi derrubado (durante a Segunda Era), a antiga forma "pura" foi esquecida por todos, menos os Nazgûl.

A linguagem que foi usada para inscrição no Um Anel foi o discurso 'puro' dos Negros (JRR Tolkien, O Senhor dos Anéis, A Irmandade do Anel, "O Conselho de Elrond" )

O Black Speech era pelo menos em parte baseado no Valarin . A Língua Negra estava incompleta e não havia poemas ou músicas nela escritas. Tolkien não desenvolveu tanto quanto as outras línguas.

The Black Speech is one of the more fragmentary languages in the novels. Unlike Elvish, Tolkien did not write songs or poems in the Black Speech, apart from the One Ring inscription.

Wikipedia

The Black Speech was not intentionally modeled on any style, but was meant to be self consistent, very different from Elvish, yet organized and expressive, as would be expected of a device of Sauron before his complete corruption. It was evidently an agglutinative language. [...] I have tried to play fair linguistically, and it is meant to have a meaning not be a mere casual group of nasty noises, though an accurate transcription would even nowadays only be printable in the higher and artistically more advanced form of literature. According to my taste such things are best left to Orcs, ancient and modern.

(J. R. R. Tolkien, "Palavras, Frases e Passagens em Várias Línguas em O Senhor dos Anéis", Parma Eldalemberon 17, p. 11-12.)

Para complementar a resposta de @ Shevilaskovic: Comum também foi usado, porque orcs de diferentes tribos não podiam se entender, como pode ser visto na passagem quando Pippin e Merry foram capturados por orcs:

To Pippin's surprise he found that much of the talk was intelligible: many of the Orcs were using ordinary language. Apparently the members of two or three quite different tribes were present, and they could not understand one another's orc-speech. There was an angry debate concerning what they were to do now: which way they were to take and what should be done with the prisoners.