The English language borrowed the word "naÏve" from French. In French spelling the letter combination "ai" always represents a single vowel sound that is the center of one syllable, while "aï" always represents two separate vowel sounds in two separate syllables. This happens in other French words too: where two vowel letters that normally represent a single vowel sound actually represent two independent vowel sounds, one of the two vowel letters is written with the dieresis (the two-dot diacritical mark) above it. Like French, English also uses a lot of combinations of two vowel letters to represent one vowel sound in one syllable, but sometimes that particular pair of letters represents two vowel sounds in separate syllables. It is common, but not required, to write that pair of letters differently in some way to indicate how to pronounce those letters. However, different words have different conventional ways to write them differently. Here are some common examples, first with ordinary spelling, then with alternative spellings to better show pronunciation: naive: naïve Noel:- Noël (a personal name, male or female) Chloe : Chloë (a personal name, female) Zoe: Zoë (a personal name, female) Rene: René (a personal name: male or female in English, male in French) Renee: Renée (a personal name, female) coop: coöp, co-op = cooperative - coöperative or co-operative Coos: Coös (a place name, a county in the US state of New Hampshire, pronounced like "COE-oss") recreate: re-create ("to create again"), distinguished from recreate "to have fun" resume: resumé (3 syllables, "summary", often summary of work experience used when applying for a job) compared to resume (2 syllables, "continue after stopping") facade: façade (most of the time "ca" is pronounced "ka", but in this word it is pronounced "sa") These are not the only words that we sometimes spell differently.

It's because it is a borrowed word from french. I wouldn't worry too much about using the diaeresis/umlaut (ï) above the "i". It's not commonly used when writing in English, although it can be. Either spelling is correct, but it is increasingly used without it.

"naïve" was a little more common in the past, but it's becoming archaic now. Native speakers will almost always write "naïve" as "naive". English dictionaries will usually spell "naïve" as "naive" also.