"Race car" covers a lot of ground. For that matter, "clutch" covers a lot of ground.
Cast iron, and high-carbon steel, are the usual choices. They may be chrome-plated. Don't see any reason for using special alloys.
The steel plates in motorcycle and automatic-transmission multi-plate clutches are clearly stamped out of flat sheet in a stamping press. The drive ears can have sharp edges on one side and rounded on the other, because of the way the stamping tools cut them out of the sheet. A lot of the time, the surface is dimpled, to give the oil someplace to go. It's easy to do that in the press tooling.
I haven't seen Formula 1 parts, nor Top Fuel dragster parts, and everything I've handled with my own hands, has been for wet multi-plate clutches - hence the commentary about motorcycle and automatic-transmission parts.
My first assumption would be to use a material with a low coefficient of thermal expansion for the best dimensional stability.
Next, I think you want a part that doesn't heat treat (harden). If it gets hot spots that cause it to air harden, that causes the material to shrink and maybe warp the plates.
EN 15 has a high enough carbon content for it to be air hardenable. If you were to look into the Nimonic series of stainless steels some have a similar coefficient of thermal expansion but don't have the air hardening issue.
