There was an elaborate system of nomenclature among the Arabic-speaking peoples in the early Islamic period. In full, each individual’s name could consist of four elements:
A ruler, a member of a ruling group or a dignitary might have a title or honorific (laqab) prefixed to his name. The Rāshidūn and Umayyad caliphs were simply known by their isms, but both ‘Abbasids and Fatimids adopted regnal titles indicating the fact that they were supported by Allah or that they were upholders of the Faith (dīn) and it is by these titles, or shortened versions of them, that caliphs are generally known, e.g. al-Manṣūr, al-Mu‘izz. From the fourth/tenth centuries onwards, members of successor dynasties used titles of the form ‘Imād al-Dawla, Rukn al-Dawla meaning “Support or Pillar of the (‘Abbasid or Fatimid) State”, and this nomenclature became widespread. For a full discussion of titles and their development, see the article Laḳab by C. E. Bosworth in the Encyclopaedia of Islam (Second edition).
The part of the name which is conventionally used by modern writers, including this one, is quite arbitrary and is more dependent on convention than logic.
The Muslim era opens with the Hijra (often spelt Hegira), i.e. the emigration of Muḥammad from Mecca to Medina in AD 622. Muslim years are therefore indicated by the abbreviation AH (Anno Hegirae). The Muslim year consists of twelve lunar months and is therefore approximately eleven days shorter than the solar year of the Western calendar. This also means that the months do not always occur in the same seasons of the year. There is no Muslim equivalent of BC dating. To find the AD equivalent to Muslim AH dates and vice versa, conversion tables are necessary. There are a number of easily accessible web-sites which will now do the conversion easily and accurately.