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A friend of mine kindly passed on a tool board to me. I've mounted it on the wall...but now I need something to hang the tools on it. But I'm not sure what to look for and where? Are they called pegs? Or hooks? Where do I find them? Any tips?!

Looks like a decent one, too. I don't have one but have a look at Bott tool board and accessories; they are The Daddy when it comes to workshop storage and accessories; they at least use the square hole system that yours does.
https://sac-bott.com/hook-kits
Not cheap and I'm sure there's cheaper alternatives.
Wow, yes a bit expensive. Nice looking though... Now to try to find some cheaper/second hand!
Maybe not the neatest solution but I wonder if you could use hooks like these (for pan/kitchen utensil racks)
try looking for 'Square Peg Board' fittings
Use some rawl plugs and long screws to fix a bit of ply over the top of your tool board, then you can use any nails, screws or hooks to fix tools to your much more useful and adaptable ply tool board.
I butchers three wire coat hangers to make some hooks for one of those many years ago. Do you still get wire coathangers or are they all plastic or wood now?
Have a look on Bigdug or Machine Mart, I'm pretty sure I've seen those boards.