Minor planet designations are number-name combinations given by the Minor Planet Center, a part of the IAU. They are used for dwarf planets and small Solar System bodies such as asteroids, but not comets. They are given to a body once its orbit is secured and unrelated to provisional designations, given when an object is found.
The two parts of a formal designation are
It looks like this: (number) Name
, for example (90377) Sedna or (55636) 2002 TX300. According to what the astronomer wants, the brackets are now often removed, as in 90377 Sedna. In practice, however, the number is primarily a catalog entry for any reasonably well-known object. Therefore, the name or provisional designation is generally used in the formal designation: Sedna, 2002 TX300.
The rule for moons of minor planets, such as the formal designation (87) Sylvia I Romulus for the asteroid moon Romulus, is an extension of the Roman numeral convention used, on and off, for the moons of the planets since Galileo's time.
The Minor Planet Center also managed comets but used a different cataloging system.