So I'll be honest, I'm not sure how to translate おやすみとん because it seems to have changed over time. The artist miton (turuyasann) often marks (original character name) after Miton-chan in the commentary on her images, clearly identifying her name. Miton-chan also appears to have a catch-phrase of "おやすみとん" which is a pun mixing "おやすみ" (Good Night) with "みとん" (her name). However, I'm seeing increased usage of "おやすみとんちゃん" and miton (turuyasann) has followed that with (original character name) a couple of times. Since "Oyasu" is a valid family name, I'm wondering if the artist adapted the catch-phrase into the character's full name (Oyasu Miton, Oyasu Miton-chan).

Else, it may just be a longer hashtag for "Good Night Miton-chan", making use of the pun. Or all of the above.

For example, the translation of the text in this image could be:
Good Night Miton-chan (Original Character Name)
Oyasu Miton-chan (Original Character Name)