Linnean is closely associated to the alternative spelling Linnaean, and can refer to any of the following all of which are related to the original system of scientific taxonomy of biological species or its author:

Linnaean

• Carolus Linnaeus
  Carolus Linnaeus
  Carl Linnaeus , also known after his ennoblement as , was a Swedish botanist, physician, and zoologist, who laid the foundations for the modern scheme of binomial nomenclature. He is known as the father of modern taxonomy, and is also considered one of the fathers of modern ecology...
  
  
• Linnaean taxonomy
  Linnaean taxonomy
  Linnaean taxonomy can mean either of two related concepts:# the particular form of biological classification set up by Carl Linnaeus, as set forth in his Systema Naturæ and subsequent works...
  
  
• Linnaean enterprise
  Linnaean enterprise
  The Linnaean enterprise is the task of identifying and describing all living species. It is named after Carolus Linnaeus, a Swedish botanist, ecologist and physician who laid the foundations for the modern scheme of taxonomy....
  
  

The Linnean Society of London

Linnean Society of London

The Linnean Society of London is the world's premier society for the study and dissemination of taxonomy and natural history. It publishes a zoological journal, as well as botanical and biological journals...

 suggests http://www.linnean.org/index.php?id=19 that the distinction in spelling is between ‘Linnaean’ referring to Linnaeus himself, his works, his classification scheme and the system of nomenclature, and ‘Linnean’ referring to the various societies and is in accord with the name von Linné, which Linnaeus adopted after being ennobled in 1761.