Where does the name ‘aliphatic’ come from?
Olefins are hydrocarbons that contain at least a double bond. The term is used &mdash;sometimes misleadingly&mdash; interchangeably with alkenes.


  Although the nomenclature is not followed widely, according to IUPAC, alkenes are acyclic hydrocarbons with one double bond between carbon centers. Olefins comprise a larger collection of cyclic and acyclic alkenes as well as di- and polyenes. &mdash; Alkene nomenclature &ndash; Wikipedia


The Goldbook page Wikipedia cites says the final words:


  Olefins
  
  Acyclic and cyclic hydrocarbons having one or more carbon–carbon double bonds, apart from the formal ones in aromatic compounds. The class olefins subsumes alkenes and cycloalkenes and the corresponding polyenes.


While Oxford dictionary seems to agree with the origin thingy:


  Origin
  
  Mid 19th century: from French oléfiant 'oil-forming' (with reference to oily ethylene dichloride).


Funny thing is, "aliphatic" also means "producing fats". Goldbook says:


  aliphatic compounds
  
  Acyclic or cyclic, saturated or unsaturated carbon compounds, excluding aromatic compounds.


Some definitions exclude alicyclic compounds from the list of aliphatic compounds, but IUPAC doesn't agree, so. Note that aliphatic compounds can be saturated or unsaturated.

So, back the main answer part,


  Aliphatic; Etymology
  
  From Ancient Greek ἄλειφαρ ‎(áleiphar, “oil, ointment”). &mdash; Wiktionary


There are literally no articles on the Net speaking of the first discovered or documented aliphatic compounds, but I read in some textbook somewhere which mentioned that since these compounds were first referred to as what animal fats used in primitive or medieval lamps were consisted of, they're referred to as "aliphatic".

The only thing about a "first aliphatic" I could find is mentioning "Muconic acid is the first aliphatic compound formed as a result of aromatic ring splitting, which is further oxidized to fumaric acid and then participates in the cell metabolism as a standard endogenous substrate." by this paper.