"Good morning, Anna."
Translation:Доброе утро, Анна.
It's not complicated, you just need to remember of gender of question, when you ask or tell. Any phrase you can check by a gender question. For example: "Зимний лес". Male gender, and control question is "КАКОЙ лес?". Last letters in КАКОЙ shows you that you need to use "Зимний" and not "Зимняя" (КАКАЯ) or "Зимнее" (КАКОЕ). I hope it helps you.
Yes ! My mother is a russian native and is herself called Anna. And she has at least 5 other friends called Anna, which is why there are so many variations used of a given name: Анна, Анюта, Анька... I don't if it still works like this, but in her time when someone was born you had to pick a name from a register of already existing names, which explains why so many people have the same one