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April 11, 2018 12:50 PM

Khloé Kardashian is due to give birth to her first child, a baby girl, any day now.

But with videos surfacing of boyfriend Tristan Thompson allegedly getting close to an unidentified woman at an N.Y.C. lounge over the weekend and sources calling him a “serial cheater,” will Khloé be naming the baby after him?

The mom-to-be’s latest Instagram photo — a snap of Khloé giving the NBA player a passionate kiss with the caption, “We are ready whenever you are little mama” — has been flooded with messages of support for Khloé as well as urges to give the baby her last name.

“Hope baby gets the Kardashian name,” wrote one fan, while another added, “Baby Kardashian not Thompson he doesn’t deserve the name.”

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RELATED: Pregnant Khloé Kardashian’s Boyfriend Tristan Thompson Is a “Serial Cheater,” Alleges Source

The Kardashians and Jenners have always given their children the father’s last name, even if they weren’t married. Kourtney Kardashian‘s three children — sons Reign Aston, 3, and Mason Dash, 8, plus daughter Penelope Scotland, 5½ — all have her ex-boyfriend Scott Disick‘s last name.

Kim Kardashian West also gave her daughter North, 4½, the last name of husband Kanye West before they tied the knot. The couple later welcomed son Saint, 2, and daughter Chicago, born on Jan. 15.

Despite relationship issues between Rob Kardashian and Blac Chyna, they gave their 17-month-old daughter Dream Renée the Kardashian surname, making her the only one of Kris Jenner‘s grandchildren to have the Kardashian or Jenner moniker.

New mom Kylie Jenner also revealed her daughter’s full name to be Stormi Webster, taken after the baby’s father Jacques Webster — known better by his stage name Travis Scott.

RELATED VIDEO: Then and Now: Khloé Kardashian and Tristan Thompson’s Relationship Whirlwind — How Did We Get Here?

Khloé seemed to be planning to follow the tradition, getting a custom neon sign for her pink-themed baby shower that read “Baby Thompson.”

The 33-year-old Revenge Body host has also been open about her struggle to pick out a name for the new addition. In January, she appeared on The Ellen DeGeneres Show, where she seemed to have a better idea of what moniker she’d settled on should she welcome a baby boy.

“I think if it’s a boy I’ll go with Junior — Tristan Jr.,” Khloé said. “Then for a girl, I don’t know where to begin.”

Though she didn’t have any girl names chosen, the first-time mom-to-be shared on Twitter that she wanted the initial to be a “K” or a “T,” after Mom or Dad.

RELATED: Pregnant Khloé Kardashian’s Family Had “Concerns” When She Started Dating Tristan Thompson: Source

But things may change in light of an alleged video of Thompson getting close to an unidentified woman Saturday in a New York City lounge. A different insider confirmed to PEOPLE that he was at the PH-D Lounge in Manhattan over the weekend ahead of the Cleveland Cavaliers’ Monday game against the New York Knicks.

A man who has been identified as the 27-year-old athlete was seen speaking closely with a brunette in photos and footage published by the Daily Mail and TMZ. The Shade Room later published a video of Thompson and a brunette allegedly entering his hotel at 5 a.m.

TMZ also posted footage recorded in October, allegedly depicting Thompson kissing one woman while a different woman groped him at the Darna hookah lounge outside of Washington, D.C.

“Tristan has been consistently cheating on Khloé,” a source alleges to PEOPLE. “He’s a serial cheater. And there will be more women to come out of the woodwork.”

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