Most people are going to use Google, maybe Bing, maybe Bahoo!, and are barely aware of and would not use another search engine.
Those that do know about DDG will either use it or not.
Whenever I include a search link in an email (or HN thread) it's always a DDG link, except for those rare searches where I get nothing back from DDG. I think that's one of the best ways to promote DDG. Bonus, the DDG search links are unadulterated.
And by the way, if you want to search google a little more anonymously, do it via DDG. In your search bar or on DDG's page, type in !g your search term. You'll be redirected to Google's search, and the URL will be relatively clean:
half the world uses the word "xerox" for a copy machine, "pampers" for diapers, and "jeep" for an offroader. So, google as verb is now completely natural
...and lawyers love people who use those words as verbs, because they get paid every time they write a letter to say that the verb is, in fact, a trademarked noun and could a different word be used, or the trademark be acknowledged?
Google used to (still does?) send cease and desist letters; and they've asked people to only use google-as-a-verb when people are actually talking about Google. Thus "I'll google it" when a person is using Bing is, according to Google, not on.