Is there a special name for a person born without any arms?

one of the names was thalidomide baby due to the fact that during pregnancy
the moyher took thalidomide

In addition to Thalidomide, there is a genetic condition known as Grebe syndrome which produces extremely shortened, or missing limbs.

'Grebe syndrome is a very rare form of short-limbed dwarfism. It is a genetic condition, passed by autosomal recessive inheritance (both parents carry a recessive gene, and 1/4 of their offspring will be affected). The largest cluster of people with Grebe syndrome are in Brazil. The condition was first described in 1952, and initially called achondrogenesis - Brazilian or Grebe type. Today Grebe syndrome bears the name of its discoverer. It is very closely related to a number of other forms of dwarfism, some of which are associated with other major medical problems. Misdiagnosis is common. In one series of three patients with Grebe syndrome (which is a lot for this rare disease) two of them later turned out to have other, more serious types of dwarfism (Journal of Pediatrics, Dec 1977).'

http://www.drgreene.com/21_845.html