Something has to replace it as an identifier. I suppose the next best idea is the one that nationalism replaced - the 'dynasty-state', where identity was more along the lines of who you recognized as sovereign. So you'd have 'Habsburg' subjects and 'Romanov' subjects and so on.
To piggy-back on this, I agree that something has to replace it as an identifier, and I think an even better replacement would be religious identity. Make religious sect really, really important, and keep it that way, and the populace's identity will solidify around shared religion and not shared cultural/linguistic ethnicity.