It is called a "mitre."
The bishop's headdress is called a mitre.
A mitre
The Bishop headdress is called a mitre.
In the Catholic Church most Bishops head a diocese.
It is a dhari (A dancer's headdress)
double crown
When viewed from the South it has an appearance like a Christian Bishop's Mitre or Headdress. Mitre Peak is in Fiordland, New Zealand.
In Eastern Orthodoxy, the Church Year or Liturgical Year is referred to as "the Indiction."
I think you're talking about a bridle.
Des Bishop's birth name is Desmond R. Bishop.
Gregg Bishop's birth name is Gregory Paul Bishop.
Sonny Bishop's birth name is Erwin Wilfred Bishop.