Answer by taking a quote from the following article:

The Romani (also spelled Romany , ), or Roma, are a traditionally itinerant ethnic group, living mostly in Europe and the Americas and originating from the northern Indian subcontinent, from the Rajasthan, Haryana, Punjab and Sindh regions of modern-day India and Pakistan. A DNA study conducted by Indian and Estonian research facilities shows that the Roma/Romani/Gypsy and Sinti people originate from the so-called "Untouchable" Dalit community from India. The Romani are widely known among English-speaking people by the exonym Gypsies (or Gipsies), which some people consider pejorative due to its connotations of illegality and irregularity. They are a dispersed people, but their most concentrated populations are located in Europe, especially Central, Eastern and Southern Europe (including Turkey, Spain and Southern France).

The English term Gypsy (or Gipsy) originates from the Middle English gypcian, short for Egipcien. The Spanish term Gitano and French Gitan have similar etymologies. They are ultimately derived from the Greek Aiguptioi (Aigyptioi), meaning Egyptian, via Latin. This designation owes its existence to the belief, common in the Middle Ages, that the Romani, or some related group (such as the Middle Eastern Dom people), were itinerant Egyptians. According to one narrative they were exiled from Egypt as punishment for allegedly harbouring the infant Jesus. As described in Victor Hugo's novel The Hunchback of Notre Dame, the medieval French referred to the Romanies as Egyptiens. The word Gypsy in English has become so pervasive that many Romani organizations use it in their own organizational names.  This exonym is sometimes written with capital letter, to show that it designates an ethnic group. However, the word is sometimes considered derogatory because of its negative and stereotypical associations. The Council of Europe consider that 'Gypsy' or equivalent terms, as well as administrative terms such as 'Gens du Voyage' (referring in fact to an ethnic group but not acknowledging ethnic identification) are not in line with European recommendations. In North America, the word Gypsy is most commonly used as a reference to Romani ethnicity, though lifestyle and fashion are at times also referenced by using this word.  Another common designation of the Romani people is Cingane (alt. Tsinganoi, Zigar, Zigeuner), which likely derives from Athinganoi, the name of a Christian sect with whom the Romani (or some related group) became associated in the Middle Ages.

What other names do they have?
the medieval French referred to the Romanies as Egyptiens.