This enzyme belongs to the family of ligases, specifically those forming carbon-sulfur bonds as acid-thiol ligases. The systematic name of this enzyme class is phytanate:CoA ligase (AMP-forming). This enzyme is also called phytanoyl-CoA ligase.
References
Muralidharan FN, Muralidharan VB (1986). "Phytanoyl-CoA ligase activity in rat liver". Biochem. Int. 13 (1): 123–30. PMID3753503.