Daisy

Daisy is Doomguy's pet rabbit.

In the classic Doom, the rabbit's head is shown in the end picture of Episode 3: Inferno, first in a docile setting, resting in a sunny field, then in an instant turnaround, decapitated and its head impaled on a pike as evidence that the hellspawn have come to Earth. The rabbit is not specifically identified as Doomguy's pet at this time.

In the end picture of Episode 4: Thy Flesh Consumed, the rabbit's head reappears in Doomguy's hand. It is here that the game mentions "someone was gonna pay for what happened to Daisy, your pet rabbit". Due to the lack of any previous mention of this in the Episode 3 text, this would appear to be an example of retconning.

Daisy is the reason why the Marine continues to fight demons in Episode 4: Thy Flesh Consumed, as it shows in the end as Doomguy holds its head in his hand, possibly stating Doomguy avenged his pet rabbit, making Episode 4 a mission of revenge and is not totally focused on stopping the invasion of demons. Nothing is really known about Daisy, or how it came to be with Doomguy, as well as its past with Doomguy or its meaning or purpose in the game other than just a cinematic ending. However, many theories have come and gone over the years, many having to do with the bunny shape on the burning building. Daisy is more or less a mere ending for the Doom series and most likely means nothing in general.

Other appearances

 * A poster on a wall in one of the Doom (2016) multiplayer levels shows an image asking for missing Daisy and offering a reward. The phone number is the original release date of Doom.
 * In Quake Champions, Doom Slayer's bio says he still angry for having lost Daisy, and carried around her rabbit's foot.
 * On July 23rd, 2018, the official DOOM Twitter released a mysterious tweet reading "justice for Daisy", leading some fans to hope that the rabbit will be included in Doom: Eternal in some fashion.
 * Daisy also appears in Action Doom in the final level. She is animated, and runs around Doomguy's house.
 * She also appears as a cheat skin of past versions of Skulltag.
 * Daisy can also be seen alive on the start-up screen of the Doom95 port.
 * A promotional image for Doom: Eternal released on June 9th, 2019 includes a rabbit hidden amongst the crowd of demons surrounding the Doom Slayer, lending further credence to the idea that Daisy will appear somehow in Doom: Eternal. Daisy does indeed make a cameo appearnce in the Doom Slayer's room on the Fortress of Doom, being held gently in his hand in a painting.
 * A painting of Doom Slayer holding Daisy can be seen in Doom Eternal. The Marine also wrote a book "My Best Friend, Daisy".
 * In Doom: Annihilation, Daisy makes an appearance as an AI. She is eventually revealed to be evil (like HAL).
 * Daisy (at least the Daisy of this universe) can be found alive and well and can be found hidden throughout every chapter of Doom Eternal.

Behind the scenes
Many state that the pike is none other than Doomguy's arm, however many discredit this as it makes little sense to as why he would do it and how the bunny got from the field to the front of the city. In truth, however, it is just a wooden spike. There are other theories stating similar things but none can be proven as not much is known about Daisy itself.