I changed the tests to give a somewhat bettwer feedback, but infortunately your solution fails only for longer inputs so it can be not that easy to debug. However, I found out that your solution fails following test case:

assert.strictEqual(nameInStr('Betty', 'Betty'), true);

Additionally, you are handling letter case incorrectly: "case-insensitive" means that lowercase letters and uppercase letters should be treated as the same.

Yoru solution is buggy, it's not a kata issue.