A possible derivation appears in The Peoples of Middle-earth (The History of Middle-earth Vol. 12): XI The Shibboleth of Fëanor. Here, Finarfin is a contraction of Finwë Arafinwë adapted to the sounds of Sindarin. The meaning would be 'Finwë, noble Finwë' (according to this source, Finwë originally named each of his three sons after himself).
It should be noted, though, that The Shibboleth of Fëanor dates from the late 1960's, suggesting that Tolkien invented this derivation 'after the event' - it appears (though this cannot be stated certainly) that the name came first, and its derivation followed years later.