That's because there's a popular musical artist called DDG with tens of millions of streams, because guided missile destroyers are designated DDG by the US military and NATO, and because not many people refer to DuckDuckGo as DDG.
If I search for "Alternatives to Google Search," I do see DuckDuckGo, including answers to questions like "Is DuckDuckGo Better than Google," with the answer being yes, it is.
If I search for "duck search", Duck Duck Go is the first option. If I search for "Privacy Search Engine", DuckDuckGo is the fourth result.
Note: The Duckduckgo site is the first result for "Duck Duck Go", you mean the string "DDG" in particular I'm presuming.
Now, it's not Google's obligation to make Duck Duck go a primary result for the DDG abbreviation - DDG the artist is apparently quite popular.
It would be nice, yes, if Google didn't just guess the best meaning for DDG but instead gave a spectrum of the common meanings (though Duck Duck Go might still not deserve to appear unless it's search became better imo).
The way that Google has degenerated over the last 5-10 years is in more aggressively showing you what they think you want rather than what you ask for (and limiting how you ask for things to boot). But after using Duck Go Go for two years, it seems they have exactly the same problem and that situation explained by them being a meta-search engine leaning on Bing (which in turn clones Google). At least Duckgogo features themselves on a search for DDG but they lean more heavily on battleship with the name.
Yeah, both Google and DDG have the "we know better than you" problem with searching. I have to aggressively use the -keyword filter on searches with both.