Jelka

The name is not a diminutive of Jelena but one of the names that derive from the word for a fir tree; "jela" or "jelka". It is the European silver fir tree to be exact.

Of course Jelka is a diminutive of Jelena (technically it's a diminutive of Jela, which is a short form of Jelena). And there is a longstanding association with words jela and Jelka, both meaning fir tree, as Anonymous user said. That doesn't mean that the form of the name was influenced by the word, or vice versa, I don't believe either is the case here.
Also, there's no need to linguistically separate jela and Jelka like it's done on this site: one name being identified as Serbian and Croatian, the other as Slovenian. In Croatia at least both forms are used, either as a first name (there are over 3000 people named Jelka) or the word meaning fir tree. Jela simply means fir tree, genus or species, while Jelka tends to specifically be used to mean Christmas /fir/ tree as, indeed, a diminutive and affectionate form of jela. [noted -ed]

I thought the origin of the name is the name of the tree. In Slovene Jelka is a fir tree.