yes, 乐乐 is a name. For 灰灰的，I believe your question is why we just say 灰的。 Acturally both are correct. But if you double the characters like 灰灰的, it sounds cuter. 灰的is more formal and used in writting.

Basically, when we repeat the characters, there are several situations. 1. Repeat a name, it's more like a nick name; 2. Repeat an adjective For example, 他的皮肤很白。→他的皮肤白白的。 It's an expression to emphasis that his skin is REALLY/VERY white. Another example, 他高高的。You can guess the meaning. 3. Repeat a verb For example, 周末的时候我喜欢看看书。“看看” means you do something leisurely, not so serious, or you do it in a short time, you won't stare at the book for a whole afternoon. Another example, 这是我做的菜，你尝尝。 Hope this will be helpful. : ) Li Ying

In Chinese，there are many strange ways of expression，灰灰的or萌萌的is just a way in spoken Chinese....we can also use萌萌哒instead of萌萌的，it is a cute way to express someone is cute...and we use 哒just because it sounds cute( •ิ_• ิ)

Repeat it twice, it sounds more sentimental to me, well, can be cuter too.

乐乐is like a nickname or a pet name