Since -el/-l is a common diminutive suffix in Yiddish (Feivel, Hendel, Koppel, Motl, Yentl, etc.), Elkel could be a diminutive of Elka or Elke. Elke is described as a Yiddish name in this sourced Wikipedia article (
https://en.m.wikipedia.org/wiki/Elke), a feminine form of Elkanah (which is already in the database as Elke(2); it is also a German name, so this theory seems plausible).
Both Elkel and Mate appear in this list (
https://www.avotaynu.com/books/dagnindex.htm). As for Mate, I don't have a theory for its etymology, but Mata, Matel and Matke appear in said list as well.
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