Wikipedia calls it 'ng coalescence'.

"This means that the words finger and singer do not rhyme in most modern varieties of English, although they did in Middle English."

https://en.m.wikipedia.org/wiki/Phonological_history_of_Engl...

> In German "ng" is always without a distinct g-sound (like German "Finger", or its n and g like "Ungeheuer")

Depends on the dialect. For example, older speakers of Swabian may totally say "Feng-ger" to "Finger", as opposed to the more "modern" Swabian variant of "Fenger".

My chorus director in college was always trying to get us to not use the /g/ when singing German. He often used the finger/singer analogy to explain the difference.