Can anyone tell me what this Heywood lounge chair style is called?  

Your chair might be the best-looking Hey-Wake piece I've ever seen (and I've seen plenty in my 60 years here in Massachusetts). The style is certainly Mid-Century American Modern. Looks comfy, too, and appears to be in remarkably good condition, possibly expertly reupholstered in an appropriate fabric.

Heywood-Wakefield did often name their lines. If that's what you're after, there should be aficionados to be found elsewhere online that can help if none pipe in here.

Nice chair. Good luck and thanks for posting!

It is part of the Aristocraft line from the early to mid 1950s designed by W. Joseph Carr.