Is there any reason why a Death Domain cleric can't use their channel divinity multiple times on the same attack?

Question

The Channel Divinity is Touch of Death, which reads as follows:

When the cleric hits a creature with a melee attack, the cleric can use Channel Divinity to deal extra necrotic damage to the target. The damage equals 5 + twice his or her cleric level.

This doesn't require any action,so is there a reason why a high level death domain cleric couldn't use it multiple times on the same attack? I get that "features with the same name don't stack", but features like the paladin's divine smite specify you expend ONE spell slot, with no such specification for this feature.

Answer 1

Only one Touch of Death applies

Neither Channel Divinity nor Touch of Death limit how many times you can use Touch of Death per attack, so you can indeed use Touch of Death multiple times per attack if you have enough uses of Channel Divinity.

However, only one Touch of Death applies to the target as described by the rules for Combining Game Effects (DMG, p252):

Different game features can affect a target at the same time. But when two or more game features have the same name, only the effects of one of them—the most potent one—apply while the durations of the effects overlap.

Specifically, using Touch of Death multiple times per attack, means that the target of the attack is simultaneously affected by more than two same-named Touch of Death features, hence only one Touch of Death applies to the target of the attack.

Answer 2

You may only use your Chanel Divinity ability once per Short or Long Rest (at Level 6, you gain one extra use, and one more at level 18).

As you mention in your Question:

"features with the same name do not stack"

So if you are a Level 6+ Death Domain Cleric you theoretically could Channel Divinity more than once on the same attack, but it would not stack with itself, and so would have no benefit above only using it once.