In the UK that is the remit of the College of Arms.

For any Discworld fans this is the basis for Ankhmorporks' 'College of Heralds'

They also organise stuff like recording pedigrees and genealogies of noble families, deciding the proper rules for flying official flags and the pomp and ceremony of big State occasions such as the Opening of Parliament.

Their staff have delightful titles such as 'Herald Extraordinary' or 'Rouge Dragon Pursuivant'