What is the expression for coughing at the beginning of an utterance officially called?
Solution 1:
In English, we would most commonly spell this utterance "Ahem." It is used to somewhat politely gain someone's attention.
It can be considered a hedge or filler, that is, a vocal delay that allows the speaker time to collect their thoughts while speaking.
I understood what you meant by "ekhm," but I have never seen it spelled that way. However, I imagine that the spelling of a word like this could be subject to regional differences.
Solution 2:
I'd just write:
Cough cough...
But, if you want the "e" version, it's actually:
Ahem! (not "e")