All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The Islamic Dinaar was only issued during the reign of 'Abdul-Malik Ibn Marwaan and the Muslims were using the Roman Dinaar and the Persian Dirham prior to that era, including the reign of the Prophet and the four caliphs. In principle it is the government that takes care of the issuing of the currency and it may order and entrust a given body to do so. The benefit of the nation should be considered when this is done. So the government may cancel any currency and issue a new one, and may determine a given category of it, and so forth; the thing which will facilitate dealing with such a currency.
This issue is an issue of Islamic politics which is based on achieving benefits and preventing harm. So, it is not possible for every person to issue his own currency, as it is unimaginable for people to deal with a great number of currencies at the same time.
Allaah Knows best.