If we allow FTL information exchange, don't we run into the possibility that the FTL accessible universe is infinite, so unique IDs are fundamnetally not possib

If we allow FTL information exchange, don't we run into the possibility that the FTL accessible universe is infinite, so unique IDs are fundamnetally not possible? Physics doesn't really do much with this because the observable universe is all that 'exists' in a Russel's Teapot sense.