You can use 段【だん】 (literally "column") to refer to the vowel of a kana. For example, エ段のカタカナ refers to エ, ケ, テ, and so on. (As an aside, 行【ぎょう】 refers to "row", i.e., consonant. ダ行のカタカナ refers to ダ, ヂ, ヅ, デ and ド.)
With this, the idea of:
Replace the "-u" with "-eru."
can be conveyed like so:
The どゃ portion
Notice that the や is basically the same font size as the ど. This is not どゃ, where the small ゃ is meant to indicate a palatalized glide attaching to the consonant of the previous mora, but rather どや. I'm vaguely familiar with the adverb どやどや used to describe lots of people milling or rushing about; I wonder if it's used here to indicate the ...
So my reasearch has been a little bit unusual for this one, but I found the following from reddit's r/learnjapanese:
Dakuten/handakuten on kana where they would normally not be found can imply a muffled, nasal, or slurred sound.
I also found some sources on this stack exchange as well. Their question was about dakuten being applied to あ.
First of all, I am also no expert, but I have been looking at classical Japanese orthography recently and noticed that many of the "spelling-change rules" seem to follow the same logic as some modern Japanese's collocations/"slang".
For example the simplifying of words by seemingly merging sounds: わからない → わかんない。If you take けふ and pronounce ふ as hu not fu, ...