When Clare Vivier opened her first Clare V. store in Silverlake, in 2012, the neighborhood east of Sunset Junction in Los Angeles was by no means a retail destination. In fact, she told me, landlords and developers tended to avoid it altogether. But things have changed over the past decade and a half: The neighborhood has become a bastion of midcentury modern mavens with record players and “rescue” purebreds—it’s basically Williamsburg West. Vivier, an American designer with French taste, is renovating the original Silverlake store, which will nearly double in size to 1,100 square feet. Clare V. has been expanding its national footprint, too.