Wrong. The chap who would have achieved prominence is more likely to have been
Charles Ferguson Smith. Both Grant and Sherman thought he would have been better than them in command. But for his infected wounded from a boat accident before Shiloh who knows...
Given that Smith was the senior officer on the ground after Grant at Donelson, he'd certainly be the most immediate beneficiary. Depending on when Grant was killed, the battle might proceed as it did in the OTL with Smith receiving Buckner's note asking for terms. Since Smith originally advised Grant to ask for an unconditional surrender, he'd definitely make the same demand himself.
What happens afterward would largely depend on whether Smith's injury is butterflied away. If it is, then you could easily end up with a replay of Shiloh, just with Smith in command instead of Grant. If Smith's injury still occurs, then it's up in the air who might end up in command. Given that Lew Wallace performed well at Donelson, he might be a possibility as a replacement for Smith if the injury isn't butterflied away.