Is the following sentence grammatically correct? Also, is this a normal usage, or would it seem weird to a native Japanese speaker?
私の友達の犬の名前は “Finn” です。
わたし の ともだち の いぬ の なまえ わ “Finn” です。
I’m hoping this says “My friend’s dog’s name is Finn” but since I’m just starting to learn grammar, I don’t know. 
Thanks in advance for any help!
Sure, you can do this. You can leave out the first 私の though, since it should be obvious from context that it’s your friend. You can also rephrase this to something like 友達の犬は「Finn」と言います if you want. It’s another way of indicating someone’s name. Instead of “the dog’s name is Finn” it’s more like “the dog is called FInn” if you were to translate literally, but this way is really common in Japanese. I can’t really speak to how natural it is to stack a lot of possessives in general though.
By the way, nothing wrong with making a new topic to ask questions of course, but also feel free to use this thread if you want: Short Grammar Questions.
Thank you! I hadn’t found the Short Grammar Questions before…I’ll have to start following that thread!