my dog has depression maybe?

Not enough information, really.

It could be insecurity....not sure of his pecking order, etc?

What type of dogs are they?
How old he? She?
How long have you had the second dog?
Who gets the most attention?
Do they go walkies together?
Does he get bullied by the new dog?
Etc...etc.

So many little factors can contribute. Normally, if you get them to do "pack" things together.....walks, fetch, sleep...and do these things as regularly as possible, they'll sort themselves out pretty soon, even if it means the odd mild scrap or two at first.

Yes...of course it can be insecurity and I think the best solution is to take your dog to your vet.