Although Frankie only gave birth to Parker in October, his moniker has come out top in a survey of more than 2,000 women.
In second place was the name of Imogen Thomas' baby girl Ariana, and in third place was Alesha Dixon's exotically named daughter Azura.
Third place went to Radio 1 DJ Fearne Cotton, for naming her baby son Rex.
Lisa Penney, spokesmum for bounty.com - who carried out the survey, said: "New parents often look to celebrities for baby name inspiration and many mums eagerly wait to find out what names celebrities have chosen for their babies.
"Already there have been 148 babies called Parker born this year and, as he was only born in October, we expect that Parker will rise up the baby names chart in the future."
Other names which made it into the Top 10 were Rochelle and Marvin Humes' choice for daughter Alaia-Mai, Nell McAndrew's little girl Anya and Shakira's baby boy Milan.
Singer Lily Allen's second daughter Marnie also made the Top 10.
Meanwhile, the name that ranked as the Worst Celebrity Baby Name in the poll was Phaedra, which Peaches Geldof called her second son. Peaches reportedly chose the name as it is inspired by one of her and her husband's favourite songs.
American singer Jessica Simpson's son's name Ace was the second least popular. In at third place in the Worst Name poll was the old-fashioned-sounding name Margot, the second daughter of Sophie Dahl and Jamie Cullum.
Other names that weren't a hit with voters include the Rooneys' choice of Klay, Katie Price's son name Jett, Kim and Kanye's daughter moniker North and Fergie and Josh Duhamel's rock-inspired choice for their son Axl.
Lisa added: "Unusual names are popular amongst mums but they do seem to draw the line at the wilder as they would probably raise a few eyebrows shouted out in the supermarket."
FAVOURITE CELEB BABY NAMES OF 2013
1 Parker – Frankie Sandford
2 Ariana – Imogen Thomas
3 Azura – Alesha Dixon
4 Rex – Fearne Cotton
5 Luna – Penelope Cruz
6 Elijah – Elton John
7 Alaia-Mai – Rochelle and Marvin Humes
8 Anya – Nell McAndrew
9 Milan – Shakira
10 Marnie – Lily Allen
LEAST FAVOURITE CELEB BABY NAMES OF 2012
1 Phaedra – Peaches Geldof
2 Ace – Jessica Simpson
3 Margot – Sophie Dahl & Jamie Cullum
4 Lula – Bryan Adams
5 Maceo – Halle Berry
6 Spike – Edith Bowman
7 Klay – Colleen & Wayne Rooney
8 Jett – Katie Price
9 North – Kim Kardashian & Kanye West
10 Axl – Fergie and Josh Duhamel
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