Oh, now I see. It's as LeksWinter says: the letter "ε" and "Ελένη" as an example of the sound.
It's actually just the letter epsilon plus the name Eleni. In order to be η Ελένη, it should have said just Eleni o "the Eleni", though the latter sound terrible in English.
Your confusion is understandable. This sentence is trying to reinforce the letter "e" and the word "Ελένη" was used to show how the "e" appears in a word. We could have used "εγώ" or "έδεσμα" or "έκει" or any other word beginning with the letter "ε".
"Ηη" means "the" and yes, we use the article "the" before names in Greek. There are 3 articles: ο/oi->masculine singular/plural, η/oi->feminine singular/plural, το/τα -> neuter singular/plural. Please note these refer to the grammatical gender of the word not the person/thing it refers to.
In addition, I must mention that this sentence was deleted from the course some months ago. Did you find it in a Strengthen Skill exercise? For further views of the alphabet please read the Tips & Notes in the unit. See on the top left of the page.