Choir or transept.
the Crossing
Slype
Transept The ground plan of many churches forms the shape of a cross. The two 'arms' of the cross are the transepts.
The Slype is a covered passage, especially one from the transept of a cathedral to the chapter house. It is famous that a Slype is a covered passageway in a cathedral or church that connects the transept to the chapterhouse.
The transverse arm, north or south, of a cross-shaped church.
Slype - found in Chambers Dictionary
This is called the 'transept' and its purpose is to provide separation between the Sanctuary and the Nave. Sometimes the transept will include an area for the choir (although a loft is more common) and/or statuary, or side altars.
Poets corner
An altar is actually called "the altar", although if there are many altars in a Church, they may be called by a specific name, like the main altar, the high altar, the side altar, the Blessed Virgin Mary altar, the altar of repose, the Blessed Sacrament altar, the St. Joseph altar, etc.
If you mean the side arms of a church, it is called "the transept". Each of the two may contain a chapel.
Sunday Express: transept