I'm having a problem where my clients' product is known by almost everybody by the trademark of their biggest competitor. For example, imagine that my client is a sticky-tape manufacturer, but everybody already calls that product "Scotch tape". Or, imagine that my client has a ridesharing service, but everybody already says "I'll call an Uber".
What to do about SEO in those cases? We are optimizing the page to target people searching for "ridesharing", but realistically, most people will just search for "Uber" when they need such a service. Can I add "Uber" or "Uber alternative" somehow to my page? It's a trademark that belongs to another company, after all. Will Google penalize me for putting another company's name in my page? Any other ideas for SEO in a case like this?