“That’s the first I’ve heard of a mushroom’s name” doesn’t really make sense. Is it meant to be “That’s the first I’ve heard of that mushroom’s name”? If so, I think it would be better as just “That’s the first I’ve (ever) heard of that mushroom”, or “(I’ve) never heard of that mushroom (before)”, or “(I’ve) never heard of a shijima mushroom (before)”.