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Let's say the party had two Lore Bards, and both used Cutting Words on a creature who tried to attack.

Does that stack, since they are separate penalties and not enduring effects (like bless)? Or would it still fall under the "same name features don't stack" rule?

They would stack because they have no duration

The rules on stacking/combining game effects states (page 252):

[W]hen 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

I would argue that modifiers to rolls do not actually have a duration and so they cannot actually overlap, so the clause about stacking effects won't apply.

This is similar to the answer to a similar question about simultaneous fireballs which argues that you would take damage twice because the spells (and their damage) are instantaneous effects without duration.

Similarly the modifier of Cutting Words does not have any sort of persisting effect that you could call a duration, it simply happens.

Because modifiers do not have a duration and nothing with a duration is causing the modifiers to occur (such as with the bless spell) two uses of Cutting Words can combine against a single attack.

A small additional note:

The actual applications of Cutting Words are not even happening at the same time. Though they would result from the same trigger the optional rules on simultaneous events from Xanathar's states:

If two or more things happen at the same time on a character or monster's turn, the person at the game table-whether player or DM-who controls that creature decides the order in which those things happen. For example, if two effects occur at the end of a player character's turn, the player decides which of the two effects happens first.

This means that the modifiers from Cutting Words would not actually get applied at the same time, it would be one and then the other. So even if instantaneous were a duration the use of this rule would make it so that those durations were not overlapping and thus the stacking effects rule would not apply.

Combining Effects

No, the rule for Combining Game Effects says that s of the same name don't stack effects while they overlap.

“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. For example, if a target is ignited by a fire elemental’s Fire Form trait, the ongoing fire damage doesn’t increase if the burning target is subjected to that trait again. Game features include spells,
class features, feats, racial traits, monster abilities, and magic items. See the related rule in the ‘Combining Magical Effects’ section of chapter 10 in the Player’s Handbook.

Similar to the fire example, Cutting Words reads:

you learn how to use your wit to distract, confuse, and otherwise sap the confidence and competence of others.

You shouldn't be able to become "more distracted and confused" on a single attack.

But it is Instantaneous

Now, Cutting Words doesn't have a duration, but in the case of cutting words they are happening at the same time, so they are clearly over lapping as they are both happening when the attack is happening (not just same round 6 seconds, but as the effect is landing). It would be hard to argue that they aren't happening at the same time as they are both reactions to the same split second action.