Yes, every magnet has a minimum of two poles, which means at least one pair of magnetic poles. Nowadays, magnets are also magnetized multipolarly, meaning they have multiple pairs of poles. The technical designations for such magnets are, for example, 2-pole (one pair of poles), 4-pole (two pairs of poles), 6-pole (three pairs of poles), etc.
Multipolar magnetization is used for isotropic magnets, which means they were formed without the involvement of a magnetic field. They can have multiple pairs of magnetic poles, which is particularly useful in applications such as revolution counting. Anisotropic magnets, which were formed in a strong magnetic field, can also be magnetized multipolarly, but only in accordance with the magnetization direction determined during magnet formation.
In general, every magnet must have an even number of poles for its operation to be effective.