Every new parent should carry out the "swings test" before naming their baby: how will you feel when shouting the child's name at your local playground? Are other parents going to snort with laughter as you tell little Clytemnestra to stop pushing Agamemnon off the roundabout, or stop Bluebell from going the wrong way up the slide? At our local park in south London, we have a Hercules, a Monty and an Otto, who often provoke wry smiles from other parents when they are being called for home.

Naming your precious newborn something so unusual is to be admired, perhaps, but it's not for me. So when our daughter was born two years ago, we agonised over her name for five days. Some names sounded so rare, old-fashioned or plain ludicrous we feared she would be ridiculed at school, but others were, we thought, too popular. And when your name is plain old Jane, which can never be shortened, you want something longer, and rarer.

After days of disagreeing over Mabel, Florence, Gladys and Clara, we narrowed it down to Isabella (my favourite) and Emily (his choice). In the end, we picked a name that sounded like a hybrid of the two: Amelia. So pretty! And a famous pioneering aviator as a namesake! And it means Rose in Arabic, another pleasing connotation. When, a month later, David and Samantha Cameron called their daughter Florence, we breathed a sigh of relief. When I call out my daughter's name in the park, it sounds neither ridiculous nor over-used – and I haven't come across another Amelia in our patch of London in two years.

But how long will that last? Last week, Office for National Statistics figures showed that Amelia is now the most popular girl's name in England and Wales, rocketing from No 16 to No 1 in five years, with 5,054 mothers giving birth to an Amelia. That's 9,281 little Amelias born in the past two years fighting to get on the toddler seesaw. By the time she goes to school, it seems, every other coat peg will have "Amelia" written underneath it. In 1904, the name Amelia was 85th most popular, ahead of Freda and Millicent, and behind Rosina. The name was 63rd in 1996 and 32nd in 2001. Maybe I should have seen it coming.

But doesn't the popularity just show our girl is a child of her time? The top names in 1904 included Mary, Doris, Dorothy and Ethel, which haven't quite joined the current fashion for Edwardian names (although Florence was also in the 1904 top 10). My mother is called Phyllis (ranked at 96 when she was born in 1944) and disliked it when she was growing up because it was so out of fashion. My name is ordinary, yet it fell out of the top 100 in the 1980s. Who calls their daughter Jane today? My sister Eleanor thought her name too unusual at school, but I envied her.

Our Amelia has already started to call herself Mimi or Mia because that's what her friends call her. To her closest family she's Bumble, like the cricket commentator David Lloyd. And when I call that name out at the swings, Hercules's mother doesn't know where to look.