It's called a mitre.
The cross is worn by the bishop as it is the sign of religious might. He is the head of the church and deserves to wear the cross as he is the "king" of the church. Instead of wearing a crown as this sign he wears a cross for his royalty withing the church committee.
One possible answer might be "panache," which refers to a plume worn by French King Henri Quatre.
Pectoral Cross.
crown
a tiara, a crown would be worn by a king or queen
Pectoral Cross
it is a headpiece worn by a bishop.
Khufu wore the red crown worn in the lower kingdom.
The mitre is the tall, pointed ceremonial hat worn by a bishop.
The mitre is the tall, pointed ceremonial hat worn by a bishop.
A bishop's mitre is the head-dress worn by a bishop as a symbol of office.Different religions have different shaped mitres. In the Eastern church they often look like turbans, in the Western church they are often tall and deeply cleft.
A laurel