Harambe, a western lowland gorilla, was killed at Cincinnati Zoo earlier this year after a three-year-old boy fell into his enclosure.
On Wednesday, Philadelphia Zoo said it would allow the public to vote on a name for the newborn.
Social media users quickly swamped the zoo with thousands of messages.
The newborn is the same subspecies - Gorilla gorilla gorilla - as Harambe.
Zookeepers, however, said the name will be put to a public poll from a selection chosen by staff members.
There has been no confirmation that Harambe will make that shortlist and the competition has not even opened yet.
That, however, has not stopped thousands of calls for the name online.
Philadelphia Zoo said they were "amazed and humbled" by the "outpouring of support and genuine excitement".
The newborn's sex is still unknown, as the baby is being held close by its mother, Honi.
Zookeepers said staff will make suggestions once they know if it is a boy or a girl - and rely on the public to vote from those choices in the coming weeks.
"We are very excited to welcome Honi's new baby," said Dr Andy Baker, the zoo's Chief Operating Officer.
"This birth is an opportunity to engage our visitors in caring about the future of gorillas in the wild."
Harambe's death in May this year, accompanied by sensational video footage of the three-year-old child in danger, made international headlines.
In the wake of the shooting, many questioned the need for killing the animal, despite the keepers at Cincinnati Zoo insisting they had no choice.
That led to a wide range of internet memes and an online campaign of "Justice for Harambe", which later became a joke in online circles.
The zoo itself said it was "not amused" by the online jokes and closed its Twitter account, after months of Harambe references being posted in response to every tweet.
Philadelphia Zoo has been inundated with suggestions to name its newborn baby gorilla Harambe after launching a naming contest.