Learn Croatian: Dobro jutro, srećo moja!

This is the Vocative case, which you use when you are directly talking to or calling out to someone. The dictionary form of the word is sreća (happiness). For most feminine nouns that end in -a, the ending changes to -o in the Vocative case.

Does sreća literally mean 'dear'?

No, the literal translation of sreća is 'happiness' or 'luck'. However, srećo moja (literally 'my happiness') is a very common term of endearment in Croatian, used just like 'my dear', 'darling', or 'sweetheart' in English.

Why didn't the possessive pronoun moja change its ending to match srećo?

While the noun sreća changes to srećo, feminine adjectives and possessive pronouns like moja (my) look exactly the same in the Vocative case as they do in the basic Nominative (dictionary) case. Therefore, it stays moja.

Do greetings like Dobro jutro also use the Vocative case?

No, standard greetings like Dobro jutro (Good morning) or Dobar dan (Good day) stay in the Nominative case. You only use the Vocative case for the specific person or pet you are addressing, which is why only srećo moja changes here.