Is there a word for "umming"?

They are called conversation fillers:

In linguistics, a filler, filled pause, hesitation marker or planner is a sound or word that is spoken in conversation by one participant to signal to others a pause to think without giving the impression of having finished speaking. [...] Fillers fall into the category of formulaic language, and different languages have different characteristic filler sounds.

[...]

Every conversation involves turn-taking, which means that whenever someone wants to speak and hear a pause, they do so. Pauses are commonly used to indicate that someone’s turn has ended, which can create confusion when someone hasn’t finished a thought but has paused to form a thought; in order to prevent this confusion, they will use a filler word such as um, er, or uh. The use of a filler word indicates that the other person should continue listening instead of speaking.

Filler words generally contain little to no lexical content, but instead provide clues to the listener about how they should interpret what the speaker has said. While there are many different reasons for using filler words, sociolinguists have identified six main reasons for doing so: pausing to give time for the speaker to gather their thoughts, speaking more indirectly in order to encourage politeness, approaching delicate topics gently, emphasizing ideas, providing clues to emotions or behaviors, and communicating uncertainty. The actual words that people use may change (such as the increasing use of like), but the meaning and reason why people use them doesn’t change.

You might not find a single word that means "verbal pauses":

Verbal pauses are when you say um, ah, uh, you know, etc. While your brain is searching for the next words to say, your mouth keeps on going and blurts out meaningless extra syllables.

Verbal pauses also include bridge words like and, but, and so. If you say one of these words and hang on it before you actually know what you’re going to say next, it’s a bridge word.

Another form of verbal pause is the repeated word. You keep repeating your last word until you figure out what to say next, like and and and.

I think you'll find that "umming and ahing" is in most dictionaries as a phrasal verb.

Ahem, I would say exclamations.

The Oxford English Dictionary agrees:

um |(ə)m|
exclamation
expressing hesitation or a pause in speech : anyway, um, where was I?