Ironically this is a bad thing for Google from a legal standpoint. If a term becomes "genericized" then it can lose trademark protection.
"Aspirin" is a famous example. It used to be a brand name for acetylsalicylic acid medication, but became such a common way to refer to it that in the US any company can now use it.
I've been using Kagi for the past few years, but I try to use a brand-agnostic language talking about web search; e.g. "I'm gonna search [the web] for it"; "Use your favorite search engine to look it up".
Likewise and if people say, "why don't you google that?" I usually reply (obviously to everyone's annoyance:-) "I don't use Google". The general response is a blank, uncomprehending look.
In Italian verbs for foreign words are almost always generated from the first conjugation (-are), which means "to google" is actually "googl-are".
With kagi, one cannot miss the opportunity to generate a similar verb " kag-are", which sounds exactly like "going number 2" (in a relatively rude way), which is what I ironically use every time I decide not to use the generic "search" verb.
I consider it one of the minor benefits of being a kagi user!
I used to. Even when I actually used DDG. Now that I use Kagi (and thus am on the second web search service after I stopped using Google) it started to feel silly so I say "search the web" these days.