Not bad; for images like the first two, consider shooting in portrait (vertical) orientation.
Okay. Thanks. Would I shoot vertical to capture more of his neck and chest, rather than JUST his head?
Your decision to turn the camera either horizontal or vertical will depend on a few things:
If what you "see" as your chosen photograph looks more vertical then turn it vertical. The same thing would apply to a horizontal format. If your intended composition "looks" more horizontal, then horizontal format would probably be best.
The other consideration would be how much of your composition actually "fits" the frame, whether horizontal or vertical. If you have a zoom lens, you can make an adjustment by zooming. If you're using a fixed focal length lens, you can do that by physically moving closer or back to frame your composition as you would like.
Additionally, you can also "frame wide", meaning; allow lots of space around your composition for cropping later. This is actually the easiest, providing that you actually remember to do the cropping, and providing you're not lowering the image quality by enlarging your shot so much that you lose detail.
So whatever looks right when you are shooting your dog. If you arbitrarily crop off part of the dog for no apparent reason, then that becomes the talking point rather than what you had intended. Anytime you get a comment about cropping off part of your subject, that's when you know you've cropped too much.
Yes, you can crop dogs and people, but the remaining composition should be able to stand on its own merit.