We have a famous song called Echad Mi Yodeya and a famous prayer "Hashem Echad".
From here we have a Hekesh of Hashem to Mi Yodeya.
What do we learn from this Hekesh?
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You only quoted part of the prayer. The entire relevant part is:
ה׳ אחד ושמו אחד לשם ולתפארת ולתהלה
Hashem is one and there's one schmo, for reputation, badges, and glory.
The connection to Mi Yodeya should now be clear.