My Japanese "name" was awarded to me courtesy of dual-sided business cards provided to me for a Tokyo company trip. My English surname translated to "Rozu." It might have been nice if they'd told me. It took me a couple of days before I understood that Rozu-san meant me.
I would never adopt a local name on my own. If while working in Spain people started calling me Pedro instead of Peter I certainly wouldn't object but I would never introduce myself that way.