What is the origin of the name of the genus Caralluma? In short, we don't know. That will not stop me writing about it.
First, I will quote from Wikipedia. I wrote this part of the entry, so I think that it is allowable.
In 1795 William Roxburgh published the name Stapelia adscendens for a plant found in India. He commented that the name for the plant in the Telugu language was Car-allum and that the succulent branches are edible raw, though bitter and salty.¹ The name Caralluma was coined by Robert Brown for a new genus in an article published in 1811. At the time he only described one species in the genus, the plant that he renamed Caralluma adscendens.²
In 1996 Helmut Genaust published the suggestion that it was sensible to conclude that the generic name is derived from the Arabic phrase qahr al-luhum, meaning "wound in the flesh" or "abscess," referring to the floral odour. Genaust was unaware that the genus Caralluma existed east of Palestine. He specifically ruled out its existence in India, where it was first described and named. Genaust presumed that the name would have first been applied to Caralluma europaea in North Africa.³
So, it is clear that the name is from the Telugu language from southern India, but what does it mean? Neither Roxburgh nor Brown seem to have recorded that and did not give the spelling in Telugu script.