Q:

What exactly is the verbal component of the Prestidigitation cantrip?

The prestidigitation cantrip may be among the most versatile spells in the whole game, and the effects that can be created with it vary widely.
Since the spell requires verbal and somatic components, we should probably assume that this applies to all of these different effects. However, if for example you want to use it in order to fool somebody or create a distraction, the verbal component might completely ruin your plan.
Has there ever been any clarification about what the verbal component is, and how it might depend on the desired effect?

A:

Verbal components are meant to be obvious
The whole reason that sorcerers can get access to subtle spell is to stop other characters from being able to see that a spell is being cast by them. Casting a spell when you are right next to someone is meant to be noticed. You'd need to use some kind of misdirection to avoid being noticed and allowing that is up to your DM's discretion.

A:

Unspecified mystic words. It's up to you
The Basic Rules on verbal components (and also PHB p. 203) state,

Most spells require the chanting of mystic words. The words themselves aren't the source of the spell's power; rather, the particular combination of sounds, with specific pitch and resonance, sets the threads of magic in motion. Thus, a character who is gagged or in an area of silence, such as one created by the silence spell, can't cast a spell with a verbal component.

This is all the rules say on what the verbal components are. Prestidigitation makes no special clarifications about its verbal component. Therefore, we are left with an unspecified verbal component. The rules provide no specific guidance, so it is up to you (or the DM) how you want to flavour your spells, including how distinguishable the components for different effects are.
However, as for whether you could fool someone, Xanathar's Guide to Everything p. 85, Perceiving a Caster at Work, clarifies that spells with components are perceptible. As for how perceptible, see this question on how loud/obvious is a wizard casting a spell. There are no clear rules on precisely how perceptible casting a spell is. If people aren't paying you too much attention they might miss the casting. Otherwise, a Sleight of Hand check might be appropriate to conceal or obfuscate the casting, at the DM's discretion.

