Yes, you are right about Steinway being very well known, but that is largely due to the two points I made above - their much greater output than (say) Bösendorfer, who produce about 500 pianos a year from their Vienna factory. The guy who sold me my piano, Marcus Roberts, reckons he sees 20 Steinway grands in and out of his business (he doesn't sell new Steinways, only old good or reconditioned ones) to every Bösendorfer.