What element is used to make permanent magnets?

There are several categories of permanent magnets.

Ordinary bar magnets are made of Iron, usually relatively soft Iron.

The metals in Alnico magnets are indicated by the pairs of letters making up the name, Aluminum, Nickel and Cobalt.  Nickel and Cobalt are the ferromagnetic materials.  Aluminum has the role of strengthening the domain walls.

Samarium-Cobalt magnets are not surprisingly made of Samarium and Cobalt

Neodymium magnets can be more expansively called Neodymium-Iron-Boron magnets for their composition.  They are the strongest of permanent magnets per unit mass at this time, and their strength comes from the rigidity and stability of the domain walls.

My main experience is with ferrite magnets.  These include natural loadstone and any permanent magnet made of Iron and Oxygen: Ferrite (magnet).  I produced ferrite magnets with hexagonal structures using Barium and Strontium.  Manganese, Zinc and Nickel are also used in producing some types of ferrite magnets.  Nearly all "refrigerator magnets" are ferrite magnets.

Generally you start with Iron, Cobalt and Nickel which are naturally ferromagnetic (they are elements that are attracted to magnets, for instance).   Iron alone can make magnets but if you alloy any of these with other elements you can make stronger magnets.

As others have mentioned Alnico (with Al + Ni + Co or aluminum nickel cobalt - cute name, huh?) is one of the older permanent magnet alloys and still common used.  More recent ones include Cobalt Samarium and Iron Neodymium Terbium "super magnets".

There are different types of magnets. For example the magnet Alnico is made of Aluminium, Nickel and Cobalt. But generally magnets are made of iron, nickel and cobalt.