Melissa as me-LIE-sa (with the vowel of "sky") is anomalous. I've certainly never heard it and it can't be inferred from the spelling.
Melissa was a very popular name several decades ago, and is virtually always pronounced me-LISS-a (rhyming with "kiss") by English-speakers in the US and elsewhere.
Do you remember the name of the cartoon?
Edit: Is it possible that the name you are recalling was
Eliza? That's pronounced with a "long I" (e-LIE-za), very much the way you are remembering
Melissa but without the M-.
This message was edited 3/19/2021, 7:58 AM