Is there a name for this kind of cap?
methinks that it is a greek fisherman’s cap.
I always thought of it as a cabbie hat.
I think it’s too wide and floppy to be a Greek Fisherman. I believe it’s called a newsboy cap. Also called an 8-panel cap, it’s sewn together out of wedge-shaped pieces. In parts of the US, it was popular a few years back among black men. I didn’t know that until I bought one. I’m a paleface, and I took a little ribbing when I wore it. 
I suspect someone is going to suggest it is a flat cap as worn by northern types such as Fred Dibnah - it isn’t.
The Greek Fisherman cap does not usually have the button or snap that holds the crown down to the brim.
With a somewhat smaller crown, it might be an Ivy cap, (sometimes called a Driving cap).
With a larger, floppy crown, it might be a Gatsby or Apple or Newsboy cap.
This outfit calls them
Eight Panel caps and Ivy caps (the former, presumably from the construction).
http://www.hatsandthat.com/shopping/shopdisplayproducts.asp?id=16&cat=Mens%2BHats
Looks like just a regular tweed cap (common in the UK) to me. Different styles can be found at the link above.
http://stores.pilotonline.com/menshats/Caps.html (Corrected link to Eight-panel and Ivy caps.
See?
http://www.harristweedshop.com/tweed-caps.html
try this tweed cap outlet
Looks like an Andy Capp cap to me.
I was thinking when the OP said “kind of cap” in more general terms. I knew I should’ve stayed out of this one. Tweed caps are not quite the style in these parts. Kinda like all cowboy hats are not alike. Sorry 'bout that.
After looking a bit closer, I can see that “style” of tweed cap is more like the 8 panel that Tom~ mentioned.
Hey, we’re all a little ignorant 'bout something, from time to time. Thanks for the education.