People nowadays probably are more acquainted with 2016 and Eternal nowadays with Doom, but the series is so monumental that honestly I think there should be a great portion of content for the original two games, which were a phenomenon back in the 90s.
Let's go over his moveset first. Doomguy wouldn't be like your typical zoner - Doomguy, despite his appearance, would be super agile with his groundspeed and airspeed. His gameplan is to get in the enemies' face and blow them away with powerful close-range implements, such as his Super Shotgun or the Chainsaw. His Explosive Barrel special serves as a mix-up that can be potentially backfired onto Doomguy with crafty opponents. It could be compared to Pac-Man's Fire Hydrant or Duck Hunt's Trick Shot, only lacking agency in exchange for a lot of power.
Doomguy's Chainsaw could be compared to Banjo's Breegull Blaster, but no projectiles are fired. It's mostly how Doomguy is able to move when using it. When opponents are caught, pressing the special button again will exit the mode with Doomguy jerking the chainsaw upwards. It capturing opponents is kinda like how it's used in the original Doom, by continually stun-locking opponents.
Where Doomguy struggles with is his recovery. The Rocket Launcher is Doomguy's up special; he'll fire it downward, granting him so recoil while in mid-air. If he makes contact with the explosion, he'll blast far up. While rocket jumping isn't much of a thing in the original Doom (at least vertical rocket jumps, anyways), it's a staple of the FPS genre, which Doomguy is supposed to represent. This grants him more agility at the cost of some %, but it's hardly much of a recovery when used without a surface underneath. Doomguy will be able to act after using it, allowing him an airdodge recovery afterwards, but his lack of a sufficient enough recovery will be his core weakness in exchange for his power on stage. Like Little Mac, but, um...less bad.
What else could be Doomguy's Final Smash but the BFG 9000? Imagine it like the Dragoon item, but with a large, powerful projectile being fired while in the first-person mode (not sure if the tracers would be there as well...maybe it'd work like it does in 2016?). It also references the FPS genre with its first person mode! I think it'd be pretty good.
Let's talk other moves. Doomguy's jab would be a simple punch, alike his fists in the original games. Think of it like Ganondorf's jab - just a reliable, get-off-me tool. His other tilts would consist of him bashing with his weapons or kicking. His Smash attacks would fire other weapons - the Chaingun could be Doomguy's Forward Smash, for example, and his aerials could also follow a similar trend. I'd keep the weapons to ones that appear in both the original Doom games and 2016, for consistency between the designs. His grabs would reference the Glory Kills of 2016 and Eternal, just as brutal as they are in those games...minus the gore, of course.
Speaking of the differences between designs, as the image says, the "Doomguy" costume would have Doomguy's original looks for his weapons, alongside having his face featured in the HUD reacting to the battle, again, like in the original games, which would be an excellent touch. 2016 would omit the face (as he's supposed to be kind of like a faceless badass in 2016/Eternal) and swap the weapons/barrel for their 2016 looks. If Doomguy has his grunts as well, these could also be omitted with his 2016 look. I can't think of many specific alternates, but they could reference enemies, power-ups, other iD titles, the collectible skins on 2016/Eternal, whatever.
Let's talk his stage! As there's not really a specific key location in Doom, something generic based off of the UAC facilities you blast through in the Doom games would be fitting. Here's my idea:
Forgive the simple look, this is just meant to get the idea across. The blue represents platforms/ground and the red marks represent doors that can be opened. While fighting, power-ups and keys would spawn on the stage. Power-ups would be the ones from the Doom franchise (Armor, Berserk, Quad Damage, Haste, etc.) granting you similar buffs to the Find Mii stage, while the keys would open up random doors which would contain power-ups, or various demons from the Doom franchise (curse those monster closets!). The stage would probably resemble the environments seen in 2016 and Eternal, though I'd get a kick if it was styled just like a Doom .wad...
Let's talk music - you can see my selection in the image up there. 2016 and Eternal have a lot of great tracks, but as they're rather lengthy and best suited for the mood of 2016/Eternal themselves, I think the more consistent, melodic tunes from earlier Doom games would be desired. I hope that despite them sometimes being ripoffs of rock/metal songs of Doom's era, they could still be implemented. Notably, I also included Sadistic and Hate Machine, tunes from the pseudo-official Final Doom (Evilution specifically) and John Romero's SIGIL, which would be great to represent the strong community behind the original Doom titles. Doom 64 and Doom 3 have their main themes as well...mainly because a lot of their other songs are super creepy and probably don't fit the high octane battles of Smash Bros. The song selections of Doom 1 and 2 are mostly personal taste, but you could probably swap them with other songs. As Doom 1/2 music are also originally MIDIs, they could use a remix - but for some songs that would remove that MIDI magic! Definitely do need a remix of At Doom's Gate, though, same with Running from Evil.
I also pondered the series logo. Could be the Slayer symbol, the UAC symbol...but I think the Doom logo itself is concise enough for the games. If Street Fighter can just use the series' initials for its logo, I can't see why Doom couldn't use its iconic logo as well.
That's about it though. Thank you for coming to my TED talk.