In the section on magic items in the DMG, under Activating a Magic Item, it states:
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. The description of each item category or individual item details how an item is activated.
Further down, under Spells in the same section, it states:
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 and caster level, doesn’t expend any of the user’s spell slots, and requires no components [emphasis mine] unless the item’s description says otherwise.
Note this emphasized text does not say material components, just components. That would suggest verbal and somatic components as well as material.
The general description of wands says nothing about command words, either:
A magic wand is about 15 inches long and crafted of metal, bone, or wood. It is tipped with metal, crystal, stone, or some other material.
Further, some wand descriptions specifically mention a command word. For example, the wand of enemy detection says:
This wand has 7 charges. While holding it, you can use an action and expend 1 charge to speak its command word [emphasis mine]. For the next minute, you know the direction of the nearest creature hostile to you . . .
So going by the tenet that in 5e, the specific overrides the general, all this would suggest wands no longer need a command word to function, unless otherwise stated. But this seems like a really strange change to make from previous editions, and I’ve scoured both the rest of the rules and the web to see if I missed something.