Perhaps most people in Germany would, but in USA it would be weird to be any more familiar with the name "Bayer" than with e.g. "GlaxoSmithKline". GSK have the good fortune of a name that doesn't regularly appear on the History Channel.
Every toothpaste brand I can name is owned by either GSK or Palmolive. All GSK ones have the GSK logo on the front of the packaging. It's quite recognisable, if only as an acronym.
Don't you know Crest or Oral-B? (I'm not sure if you are talking about the US, the comments you replied to were about the visibility of the GSK brand in the US).
I find also a bit surprising that you refer to Colgate-Palmolive as Palmolive. The short name used by the company is Colgate.
Denying people you held as slaves compensation will do that sort of thing yes. Not to mention the "medical tests" on prisoners which they bought from the SS.
People don't know that much about Bayer, it's not a firm which makes often the news. Monsanto however is one of the firms with the most negative public opinion in the world, it's easy to see why they would want to scrap that name.