dnd 5e – Does dealing 0 damage to a concentrating spellcaster require a saving throw?

Taking 0 damage is taking damage: the DC 10 saving throw is triggered.

The Sage Advice Compendium explicitly clears up that you can take 0 damage. 0 is the damage minimum.

Sage Advice Compendium V.2.3 (11):

Can damage be reduced to 0 by resistance or another form of damage
There is no damage minimum in the rules, so it is possible
to deal 0 damage with an attack, a spell, or another effect.

The rules on concentration state, in part (PHB 203-204):

Taking damage. Whenever you take damage while you are concentrating on a spell, you must make a Constitution saving throw to
maintain your concentration. The DC equals 10 or half the damage you
take, whichever number is higher. (…)

Taking 0 damage still counts as taking damage and thus interrupts your concentration. The DC is 10.

Dealing 0 damage might sound unintuitive because the outcome is that you are at the same Hit Points (PHB 196) that you have had before:

Whenever a creature takes damage, that damage is subtracted from its
hit points.

But this is merely from a mathematical mindset, from a plain English standpoint you still take damage (and subtract it). That your hit point total doesn’t have to change is emphasised by looking at receiving damage to temporary hit points Sage Advice Compendium V.2.3 (13):

If I have 10 temporary hit points and I take 30 damage from an attack while concentrating on a spell, what is the DC of the
Constitution save to maintain my concentration?
The DC is 15 in that
case. When temporary hit points absorb damage for you, you’re still
taking damage, just not to your real hit points. In contrast, a
feature like the wizard’s Arcane Ward can take damage for you,
potentially eliminating the need to make a Constitution saving throw
or, at least, lowering the DC of that save.

So unless a game effect specifically calls out that it absorbs damage like the Arcane Ward does (PHB 115) or changes the recipient like the Aura of the Guardian (XGtE 39) et cetera eliminating the need to make a saving throw, then you still need to make a saving throw even when the damage does not change your actual hit points.