Trademarking and Branding

Guys, I have a question that I’m a little iffy on. If for instance I want my Amazon Brand to be “Anderson’s Pet Supplies”, would I trademark the word Anderson or all of it, “Anderson’s Pet Supplies”??

Under “Anderson’s Pet Supplies” I want to sell products like dog collars, leashes, etc. So the leash would be for example “Anderson’s Dog Leash” or the collar would be “Anderson’s Dog Collar”. I’m not going to for example name the individual products like “Anderson’s Pet Supplies Dog Collar” or something like that, that’s too long.

So am I looking for a trademark for “Anderson” or “Anderson’s Pet Supplies”??? What would I do?? Thank you in advance!!!