The couple welcomed their baby girl - a sister for 22-month-old Theodore - into the world on 22 July and have now revealed her moniker, which they chose long before the tot was born.
Vogue said: ''When we were discussing names I thought, 'I want to want her name', and I do. I just love it. I wish I was called it myself.
''We decided on it ages ago and as soon as we saw her, we knew it suited her. She is so perfect. I am obsessed with her.''
Spencer added in an interview with Britain's HELLO! magazine: ''I always really liked the name Margaux for a girl, spelt in the French way - like the wine.
''When people ask what she's called I always say Gigi Margaux - like my dad introduces me as Spencer George sometimes. It rolls off the tongue nicely.''
While she's only a few weeks old, Gigi already has an extensive wardrobe.
Vogue said: ''I've always, always wanted a little girl - I mean, her wardrobe is already quite extensive. I hope nobody buys me any more baby clothes because we've definitely got enough until she's 18 months. I couldn't help myself.''
Though Theodore has had some ''jealous'' moments since the arrival of his sister, his parents hope the fact he's been ''spoilt rotten'' by their loved ones will make him feel better.
Vogue said: ''He's been getting a lot of presents off a lot of people. It's like Christmas in this house.
''We want him to feel special, but actually, he's been spoilt rotten. He loves his sister though, and he says 'Baba!' He loves holding her.
''Though he had a couple of quite jealous days at first, and when I'm feeding her he sometimes gives me a little pinch.''
The 34-year-old model had a smooth delivery and she and Spencer, 31, are amazed at how easily Gigi has fitted into their lives.
Spencer said: ''The whole thing was alarmingly unstressful. It felt like I was going out to get a coffee.
''Don't get me wrong, we share all sorts of wonderful moments where we're just gazing at Gigi adoringly, but it does feel super smooth and straightforward this time...
''It doesn't feel like there's been any change to our life, other than the fact that we have a beautiful daughter. I love her very much and I am extremely proud of Vogue. But life goes on.''
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