I thought the dog we have as a companion at Red Rocket was Dogmeat. I know he is just called Dog so I thought that was it. After reading a few non spoiler threads, since I don't want any spoilers, I thought I read that there is an actual dog named Dogmeat.

So without any spoilers, is Dog we meet at Red Rocket at the beginning of the game, Dogmeat and is the only dog, or he is not Dogmeat and we find him later (please don't say where if it is, just a yes will do ) and there is other dogs in the game and we can choose which one we want as a companion.

ask mama murphy about "dog"

There are a few dogs in the game. As for dog/dogmeat he is the same thing I believe.

I've seen 3 types so far, maybe 4 not sure if they are the same breed though.

Yes, this is definitely question for mama Murphy.

Dog and Dogmeat are the same animal, you need to talk to Mama Murphy. I have met another "Dog" along the north edge of the map, headed east. I found a crazy old Paladin and gave him some Brotherhood Holotags. After that I continued a little east to cross a shallow creek and a skinless dog was hurt. I gave it some love and it went on its way.

But... I passed by there again without a companion hoping to have Skinless Dog as my friend but now there were 6, not friendly skinless dogs instead.

I have also noticed that if I walk into a room and set off a mine, reload and go back into that room the mine may not be there. I wonder how many things reset like this and how often.