Allifair, alternatively spelled Alifair or Alafair, has a very interesting history. This baby girl name suddenly popped into existence around the mid 1800's, with no mention why.
Some history buffs may be familiar with the Hatfield/McCoy "New Year's Day" Massacre, in which a long-time hatred between families (including Union vs Confederacy differences) finally escalated into an all-out violent battle. Allifair was the name of Randolph McCoy's daughter, who suffered from Polio as a child but remained productive. During an attack on the McCoy home, Allifair was shot and killed. There was later a legal trial for her murder. Ironically, there was an Alifair Hatfield born in 1873 in Kentucky.
Allifair McCoy was born in 1858, so how did she get her name? There are records of others in 1809, 1815, 1819, 1831, 1870, 1883, 1920 and 1923. 1767/1787 seems to be the earliest it was recorded. It could come from Alfher/Alvar/Aelfhere, a masculine Germanic name meaning "elf warrior," or Allovera, which is possibly an Old Germanic variant of Elvira, meaning "all true." There's also Allfry. But then, how did it jump from ancient Germanic times to early America, and continue into [rare] use today? Maybe it formed out of Elvira (popular in 17th/18th cen. lit), Alvera or Alfreda, or even Alfie as a nickname for Alfreda, which were all being used. There's even a possibility it comes from Olaf (from Aleifr) or Alastair, though less likely. And there's a chance it came about from a surname. All of the names were so rare, though, that it is hard to say. The -fair spelling seems to indicate English. Good old White Pages has linked the name to Alfreda and Alvaro as I suspected (confirming about 15 Alifair, 40 Alafair, 2 Allifair). It can also be found as a surname.
*Upon closer inspection, I have found records of women named Alifair or Elvira and using both names.
Mystery writer Alafair Burke was born in 1969. Alifair Skebe is a current writer.
There is a French band (duo?) called Alifair.