I believe it’s maybe called the IW3 rocking chair, although I’ve only heard it called that recently, so maybe that’s not correct.
It is designed by Illum Wikkelso and was made in Denmark for Niels Eilersen around the 1960s.

I've had a number of these lovely chairs over the years.
This one is undoubtedly the best I’ve had.

The paintwork is almost entirely intact, and it looks like it’s the original paint.
It comes complete with its original Danish Furniture Makers badge, always a sign of quality of make and design.