Name for 'mmm' sound
Solution 1:
Well it depends on the kind of mmm we would be talking about, but I call at least some of these sound a murmur.
a : a low indistinct but often continuous sound
b : a soft or gentle utterance
(The on-line Merriam-Webster)
Solution 2:
The Mmmm syllable can be several syllables, with many conventional meanings,
like MMM-mmm or mmm-MMM, which can respectively be 'no' and 'yes' in many contexts.
It's described phonetically as a syllabic voiced bilabial nasal continuant;
in IPA it's [ṃ] (Unicode 1643; UTF8 E1 89 83; Latin small letter M with dot below).
Similar to the [ṇ] as in certain /'sərtṇ/, which is a syllabic voiced alveolar nasal continuant.
If you turn off the voicing at some point, you can put an /h/ sound anywhere, like MMM-hmmm; this can be done without moving the tongue, since voicing is controlled through the larynx and uses no other musculature.
The one that means "this is delicious" would be classified as an interjection,
or as a conversational particle, like uh-huh, Really? and the like.
Solution 3:
In the 1974 Mel Brooks film, Young Frankenstein, there is a famous scene where this is referred to as the "Yummy Sound." Maybe not an authoritative source, but entertaining nonetheless.
Solution 4:
Mmm, this cake is delicious.
Mmm is an interjection, formed by means of onomatopoeia:
the formation of a word, as cuckoo, meow, honk, or boom, by imitation of a sound made by or associated with its referent.
a word so formed.