The origin of naïve is Latin (from the word nativus), and the dots above the “i” are a diaeresis (dots over the second vowel).
The dots above burhan’s “Önme” are an umlaut (dots over the first vowel).
If you are a reader of The New Yorker, you will see frequent uses of each, especially this year where the words coöperate and reëlect made appearances in many articles.
I think people are apt to run across the umlaut most often at the supermarket in the ice cream aisle, when deciding whether or not to splurge on a pint of Häagen-Daz.