How are cyclones categorized and how are they named?

Categories of cyclones:

Indian Meteorological Department (IMD), classified the low-pressure systems in the Bay of Bengal and the Arabian Sea on the basis of maximum sustained wind speed.

Naming of cyclones:

• Weather forecasters give each tropical cyclone a name to avoid confusion. In general, tropical cyclones are named according to the rules at regional level.
• In the Atlantic and in the Southern hemisphere (Indian ocean and South Pacific), tropical cyclones receive names in alphabetical order, and women and men’s names are alternated. Nations in the Northern Indian ocean began using a new system for naming tropical cyclones in 2000; the names are listed alphabetically country wise, and are neutral gender wise.
• The common rule is that the name list is proposed by the National Meteorological and Hydrological Services (NMHSs) of WMO Members of a specific region, and approved by the respective tropical cyclone regional bodies at their annual/biennual sessions. 

Further Reading:

• Tropical Cyclones
• Temperate Cyclones