Ancient
Arabs divided Arabia into sham which means north(combined countries of
Syria,
Jordan,
Lebanon and
Palestine) , and
Yemen meaning south, the name stuck over the centuries.
Debaters have 2 theories over the meaning of Yemen, the first means right since Yemen is also Arabic for right, Yemen would lay to the right if one would face Meccah to the east. The second means south. The latter theory gained more acceptance than the former.