Famous playwright in western medieval period?

Hrotsvitha was very early. She was a nun.

Hildegard of Binged was another nun, who was famous for writing plays, at least one of which was set to music she composed.

The Wakefield Master, whose identity is unknown, wrote some plays in the Wakefield Cycle.

John Bale was an English playwright who wrote a verse play on the life of King John in English.

Adam de la Halle was French. He wrote a musical play, "The Play of Robin and Marion."

Most medieval playwrights were anonymous.