The 'Thinking Out Loud' songsmith agreed to serenade the Little Mix beauty as Rixton frontman Jake proposed to her on stage in July on the condition he could pick the moniker for their child.
Jake told Ed he could have the honour in return for the favour but he and Jesy will only let him select the baby's second name.
During an interview on KISS FM UK Breakfast Show, Jesy said: ''He said to Jay that he would do (the proposal) and then he was like, 'But only if I can name your child.' And Jake was like, 'Well maybe not their first name, you can give them the middle name.' ''
The 'Black Magic' hitmaker and her bandmates - Perrie Edwards, Leigh-Anne Pinnock and Jade Thirlwall - are gearing up for the release of their third album 'Get Weird' and are enjoying their most successful ever period.
Although the four girls are having the time of their lives making music, they would be prepared to take a break like their pals in One Direction if they felt they needed a rest from the pop world.
They said: ''If we're ever at their (1D's) level and we'd like a break, it would be lovely! We haven't scraped the surface of what we want to achieve yet. Like we've ... We have achieved so much but we want global success.
''We just love having each other's company, like we're the best of friends, like there's just not one of those annoying people in the group that just has that big ego or anything. We don't have that in this group, like we are all ... Equal. We don't try outdo each other. We're just all try and live our dream and yeah.''
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