There's obviously an element of racism and typecasting in it, but I don't think it's necessarily limited to that. Some names sound more 'showbiz' than others, hence they get changed.
Anna May Bullock, David Spencer, Thomas Woodward, Rita Crudgington, Harry webb - all of these sound like perfectly normal western/English-speaking names - but Tina Turner, Ricky Valance, Tom Jones, Cheryl Baker, Cliff Richard just sound more 'starry', partly because they flow more naturally. And if you're primarily looking to find fame in the UK/US or other English-speaking western nations, it's only natural that there will be a bias towards what those demographics find easiest and most pleasing/showbizzy to hear and say.
The likes of Dave Dee, Dozy, Beaky, Mick & Tich and Peter, Paul & Mary were considered quirky, bland and uncool-sounding in a way that 'The Who' or 'The Rolling Stones' most certainly weren't.
Indeed, racism (or at least unfamliarity with other cultures and their styles of names) plays a part, but if Rita Crudgington had been born Fatima Al-Mukhtar and had been similarly advised or chosen herself - as a UK-based artist - to go professionally as Cheryl Baker, because it trips off the tongue more easily and sounds more showbizzy, would that really be any different?