There are various names for the canvas interfacing that traditional tailors use.
Tailor's canvas; hair canvas; hymo; and I'm sure there are others. The best are made from animal wool or hair, but many have some cotton or linen.
Tailor's canvas - but there are less expensive options.
One of the reasons there's more than one name for the stuff is that there's more than one type of canvas that's used. And in the top quality suit jackets, it's usual to use more than one type of canvas on the same jacket. Traditionally, they were made with a linen warp, and horse hair weft; modern stuff is wool or wool/nylon warp. Different sorts of hair are used for different effect: tail hair is stiffer and springier than mane hair. Hair wrapped in cotton is softer than either; a worsted spun hair yarn is softer still. Worsted goat hair is stiffer than that, but less than single filament horse hair. And not every weft pick has to be the same fiber; hair alternating with worsted wool is common. And the pitch of the weft picks is variable, as well.
You'd expect to find stiffer pieces in the shoulders, which need the most structuring, and softer stuff in the rest of the front, possibly with stiffish stuff in the lapels (for a good roll), depending on how expensive the suit is, and what the intended style is. Some of the Saville row houses do things like put multiple pieces of canvas together, with the pieces at different bias angles. Most moderately priced jackets don't have any real canvas at all. There's some sort of floating piece for the shoulder and extending down a bit, but it's not going to be real hair canvas.
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