In Cultist Base, the third level of the game, you can find three Dopefish from the Commander Keen series. The first is hanging from a rope, the second is stuck in a cracked ice wall, and the third is on a hidden cave, placed on an altar in a little shrine.
Contributed by ZpaceJ0ck0
In the initial release of "The Ancient Gods - Part One" DLC on October 20, 2020, pressing the dedicated Chainsaw button four times while on the Runes tab of the Dossier would bring up an altered logo for the game reading "Doog Eternal". This is a reference to Inugami Korone, a Japanese Virtual YouTuber who livestreamed Doom 64 and Doom (2016) in the past. She enjoyed using the Chainsaw weapon and she was nicknamed by her community as "Doog Slayer" (a play on the fact that her model is a humanoid dog).

Three days later, the Easter egg was removed from the game in the Version 3.1 update. The patch notes acknowledged the discovery, but the reason why it was removed remains unknown:

"The DOOG easter egg has been removed, but will live on in infamy… We were wondering how long it would take for someone to notice, and as always, we're impressed with the community's speed!"
Contributed by MehDeletingLater
On the bookshelf located in the Fortress of Doom, there is a book titled "How to Comb your Mustache" by Cliffton M. Fischbach, the father of YouTuber Markiplier, who passed away due to lung cancer. The developers included his name as an easter egg in the game because Mark Fischbasch stated that his father got him into the very first game in the series.
Contributed by Tuli0hWut
When asked by GamesBeat what the word "Eternal" meant in this game, creative director Hugo Martin described the word "Eternal" as an "eternal struggle for the good and evil. It's meant to symbolize that there's always going to be demons and there's always going to be a slayer."
Contributed by GamerBen144