Every single ability user in bsd has their own spider variant, however they can't coexist cuz each universe is only allowed one spider hero. However in spider Atsushi and spider Akutagawa's universe (earth 5541) they're both spider heroes that's because Akutagawa is an anomoly.
Anyways here are potential names of each spider hero and some info (btw each universe works differently unless stated. Each universe has different settings, laws, and structures)
Atsushi as Spider-Tiger: posessing both the abilities of a spider and a tiger he can turn his limbs into tiger limbs just like in the anime but he can't turn into a tiger completely. Because he has both tiger and spider abilities his senses and strength alongside his healing are twice as enhanced than regular spider abilities.
Akutagawa as Spider-Diablo (stupid ass name he picked for himself, thought it sounded cool): He work as a vigilante hero but often times work with Spider-Tiger. He has a sentient cape called rashomon that acts similarly to spider legs. Rashoumon can do almost everything it can do in the anime except use demonic armor (on demand). demonic armors abilities are a whole different story :)
Dazai as Spider-man (or Spider-moron as the locals call him): He's been spiderman longer than anyone else in the bsd cast and boy is he tired. He can no longer k!ll himself because of his spider abilities so he continues to become the citys disaster hero instead. He's been doing a terrible and lazy job at it hence the insulting name, but my guys been through a lot leave him alone.
Chuuya as Spider-Flux: Is a test subject at a government lab facility. He was experimented on and thats how he got his spider abilities mixed with gravity control. His abilities are very faulty and sometimes he cant control it so he has to wear gear that helps him surpress his ability. His powers give him immense powers making him the strongest out of all the cast but through the cost of severe pain. He works for the government against his will as their weapon.
Kyouka as Demon-Silk: Instead of having demon snow she is demon snow. she posesses the powers of demon snow while still being a spider person. She's like a ghost who can disappear and fly, she uses graceful movements as her battle techniques. She uses kunais that she attaches on her web to throw as weapons.
Yosano as Widow of Death: Just like in the anime she has the ability to heal people from the brink of death, but she's also a merciless killer. However in order to heal someome she has to bite them with her spider fangs, her venom is used to heal instead of killing.
Gin as Shadow-Web: In this universe Gin is the one who gets bitten instead of Akutagawa and she becomes Shadow-web a vigilante who works under the shadows and tries to uncover all the dark secrets and criminal organizations in the city. Her webs are made of UV and can cut through anything.
Kenji as The undefeated Spider: He as the usual spider powers but what makes him different is his strength. He's physically stronger than anyone in the spiderverse including Atsushi. And unlike most spider people he's not necessarily a hero who fights bad guys and saves people but instead helps others through their daily life using his strength. He lives in the province where crime rates are low, he occasionally helps beat bad guys in the city and not once was he defeated.