Learn Turkish: Adam merhaba diyor. - The man is saying hello.

The root of the verb is de- (to say). When we add the present continuous ending -yor, a rule called vowel narrowing happens. Wide vowels like 'e' at the very end of a root change to narrow vowels like 'i'. So, de- changes to di-, giving us diyor.

Why isn't there a word for 'the' before Adam?

Turkish doesn't have a specific word for 'the' (a definite article). The word adam alone can mean 'a man' or 'the man'. We rely on the context of the sentence to know which one makes the most sense when translating to English.

Does merhaba need an object ending since it is what the man is saying?

No. When you use the verb demek to report speech, you simply insert the exact word or phrase being said. It acts just like an invisible quote, so you don't add any extra case endings to merhaba.