Yes, it’s possible, but you had for some reason put the )}) part (that closes the require call, the interpolated value, and the CSS url) in the wrong place:
{
background: `url(${require(`../../assets/${edge.node.name.toLowerCase()}.png`)}) center no-repeat`
// ^^^
}
That said, it’s probably a bad idea as it doesn’t exactly make the code readable. Better use a variable:
const bgurl = require(`../../assets/${edge.node.name.toLowerCase()}.png`);
… {
background: `url(${bgurl}) center no-repeat`
}