Same for me. The first associations with "Bayer" in my head are "Aspirin" and "Leverkusen" (because of the soccer club Bayer Leverkusen).

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.

Bayer is a household brand in the US, for aspirin. I can’t think of any equivalency in GSK’s portfolio.

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.