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Shadowfell Brand Tattoo, the new magic item from Tasha's has this effect:

Shadowy Defense. When you take damage, you can use your reaction to become insubstantial for a moment, halving the damage you take. Then the reaction can't be used again until the next sunset.

Does this reduction stack with reduction from having resistance?

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They stack.

The rules for resistance say:

Multiple instances of resistance or vulnerability that affect the same damage type count as only one instance. For example, if a creature has resistance to fire damage as well as resistance to all nonmagical damage, the damage of a nonmagical fire is reduced by half against the creature, not reduced by three-quarters.

But Shadowy Defense doesn't grant resistance at all, so there is no reason it cannot be used in conjunction with another feature that grants resistance. It should also be noted that resistance is applied after Shadowy Defense:

Resistance and then vulnerability are applied after all other modifiers to damage.

The "same name" stacking rule is a red herring.

Citing the "features with different names stack" rule is something of a red herring: two features with different names that both grant resistance would not stack because resistance never stacks, no matter the source. Shadowy Defense stacks with resistance because it is not resistance, not because it has a different name than some other feature.

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Damage reduction is not damage resistance so they stack.

Only game effects with the same name don't stack:

[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.

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