Magical wands need to be held to cast their spells.

Does holding the wand count as a material component for the wand's spell?

And if a command word needs to be used, is it considered a verbal component for the spell?

This matters for features such as Subtle Spell, Archdruid, or to identify a spell to Counterspell.

Casting a spell from a wand requires no components

Some magic items allow the user to cast a spell from the item, often by expending charges from it. The spell is cast at the lowest possible spell level, doesn't expend any of the user's spell slots, and requires no components, unless the item's description says otherwise. (DMG Chapter 7 "Activating an Item")

Wands are magic items and that means that no components are required for spells cast from them unless the wand's description says it does (and I don't know of any that do).

If a command word or action is needed to activate the magic item, that is a separate thing from spell components completely.

Activating some magic items requires a user to do something in particular, such as holding the item and uttering a command word, reading the item if it is a scroll, or drinking it if it is a potion. (DMG Chapter 7 "Activating an Item")

Activating a magic item must happen before the spell within it is activated. And if the spell explicitly requires components, those will be required in addition to any activation requirements.

Does holding a wand and speaking its command word count as V/S/M spell components?

Maybe. Depends on the requirements of the spell. Not all spells require all three. Not all material components can be replaced.

Since you're mentioning a command word, I'll assume you're talking about a magic wand like the Wand of Fireballs (which doesn't have a command word and can only be used by spellcasters, but whatever). To understand it better, let's change the context:

A sorcerer wants to cast Fireball, a spell they know. According to the Player's Handbook, pg 203, they utter an incantation (feel free to make it up), they make some sort of gesture with a hand that isn't holding anything, and the other hand grabs a bit of bat guano and sulfur from a component pouch, they expend the needed spell slot, and fireballs result. If the sorcerer can't say anything because they're in an area affected by a Silence spell, they have their hands full of daggers, or they left their component pouch at home, or they're out of usable spell slots, they can't cast the spell. Now if they have a relatively inexpensive arcane focus like a crystal or wand, they can use that instead of the bat guano and sulfur, but they still need to have spell slots, be able to make the gesture with a free hand, and say the words out loud. Using the magic wand called the Wand of Fireballs, the sorcerer would be able to save spell slots by using the wand's charges instead of their own spell slots and the material component is replaced by the wand, but the verbal and somatic components required stay the same.

Does holding the wand count as a material component for the wand's spell?

That's a really awkward way of saying it, but basically, yes. The wand replaces the material component, unless the spell's material component has a cost specified.

And if a command word needs to be used, is it considered a verbal component for the spell?

I'd say Yes. There's only one Magic Wand in the DMG that mentions a command word: the Wand of Enemy Detection. Since the effect of the wand isn't to cast a spell available in the traditional spell list, presumably the "spell" it casts is either verbal-only or verbal and material (with no somatic component).

This matters for features such as Subtle Spell, Archdruid, or to identify a spell to Counterspell.

I think you meant Beast Spells and not Archdruid.

From the Sage Advice Compendium:

If a sorcerer casts a spell with only verbal or somatic components using Subtle Spell, can an opponent use counterspell against it?

If a spell that’s altered by Subtle Spell has no material component, then it’s impossible for anyone to perceive the spell being cast. So, since you can’t see the casting, counterspell is of no use."

S means somatic. It's a physical action required other than will/words alone that activates the spell.

M means material. Not all spells cause a material component to vanish - some use holy symbols which are used again and again. A wand can be deemed by a spell to be a reusable material component.

Simply holding a wand is not a somatic component, but waving it in a certain way, or picking it up, wielding it, pointing it, etc., if these are required gestures to cast the spell, then they fit the requirements for somatic. A spell that paralyzes wizards but allows them to speak, for example, might allow them to cast verbal spells, but if their wands had to be pointed or waved to activate, that paralysis would prevent those wands from activating.

The fact that some wands are actually magic items does not prevent them from being used as material components. Some exotic spells traditionally required enchanted items as their components.