Campaigner Charles Ross started the petition against the Duke and Duchess in July and it has been signed by more than 3,700 people.
Pushing his plight, Charles wrote: "We the undersigned petition Brighton & Hove Council to reject the usage of the titles 'Duke of Sussex' and 'Duchess of Sussex' by the individuals Henry ("Harry") Windsor and Rachel Meghan Markle as morally wrong and disrespectful to the county of East Sussex.
"As residents of Brighton and Hove we call on Brighton and Hove Council to not refer to these individuals by such titles which we believe to be entirely non democratic and symbolic of the oppression of the general public by the wealthy elite.
"Neither will Brighton Council invite or entertain these individuals nor afford them any hospitality or courtesies above and beyond that of an ordinary member of the public."
Royal fans have since spoken out, condemning the petition.
Thomas Mace-Archer-Mills, founder of the British Monarchists Society, said he was appalled by the petition.
"We are utterly dismayed that said petition has been signed by so many," he told The Argus.
"This certainly highlights that Brighton and Hove is a hotbed of Republican dissidents and is now proven to be so.
"Such a petition shows utter disdain and contempt for The Crown, not to mention copious amounts of disrespect to, and for, the Royal family which undertakes thousands of engagements per year on behalf of the nation, in right of Her Majesty as The Crown.
"This petition wreaks of republican drivel and lacks any real substance and intelligent reasoning. It truly seems to be an erratic and emotional outburst of self-loathing directed at two popular members of the Royal family.
"Next will be the 'off with their heads' scenarios and further republican sentiments which will not just culminate in petitions, but another campaign funded by socialist republicans.
"The petition also states that it is the wish of the petitioner that the Duke and Duchess of Sussex not be afforded an invitation to visit, be entertained or extended any courtesies beyond that of an ordinary member of the public.
"Like it or not, the Duke and Duchess are an extension of The Queen, the Head of State of this nation, of which Brighton and Hove are a part.
"To deny the Duke and Duchess of Sussex is to deny representatives of the Monarch and by extension The Crown - this is dangerous territory to navigate for the county of East Sussex collectively. Is Mr. Ross openly condoning and outlining the incitement of a second English civil war?
"These republican petitions may seem small, and the greater population may not take notice now, but such movements are dangerous and treasonous in the eyes of The Crown and a greater portion of the British population. Such movements seek to overthrow our system of governance and operations, warning signs that the greater British population can not ignore.
"This nation is and will remain a monarchy until the people collective say otherwise, regardless of small pockets of republican extremists such as in Brighton and Hove.
"Brighton itself has a very good and especially historic relationship with The Crown, from George IV to William IV, even to Queen Victoria whom sold the Royal Pavilion to the city. There is much to celebrate about the Royal ties and history of Brighton to The Crown. Despite all the good associated with the monarchy and the current members of the Royal family, such as the Duke and Duchess of Sussex."Brighton and Hove should not pander to minority treachery and should not further entertain such a petition as proposed.
"It would truly be a shame for Brighton to be known as the first openly hostile city towards the Royal family, which would certainly see a possible boycott of business activity and tourism related visits occurring in this royally historic seaside destination.
"Such consideration of this disgusting petition is nothing short of a slap in the face of the many decades of which Her Majesty has served the good and loyal people of Brighton and Hove. I am sure that any respectful person within Brighton and Hove would refuse this petition and anything of the sort."
Brighton and Hove residents took to Twitter to condemn the petition, calling it an "embarrassment".
"Seriously!!! Mr Ross get a f****n life," one resident tweeted.
"I live in Brighton and you don't speak for me."
Another said: "What a joke people need to get a grip."