Short answer: it is usually normal. Many dogs like to stay close to their people. It becomes a concern only if your dog panics when you are out of sight.
What the AKC says
The AKC says dogs who follow their humans everywhere are often called Velcro dogs. It says the trait is prized and bred into some dogs, especially those bred to work side by side with people. The big difference between a Velcro dog and a dog with separation anxiety is that Velcro dogs prefer to be glued to their owners, while dogs with true separation anxiety panic when they are away from their owners. Velcro dogs may be more inclined to develop separation anxiety.
What to do
If it does not bother you, enjoy it. If it does, teach your dog to settle on a bed. See a dog who follows you everywhere and panic when you are in the bathroom.
Get the right help
If your dog drools, paces or cries when you leave the room, ask a qualified professional about separation anxiety.
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Sources
Sources & care notes
Frequently asked questions
Why does my dog follow me into the bathroom?
Many dogs simply like staying close, and some breeds were shaped to work right beside people.
Is it a problem?
Not if it does not bother you or the dog. It becomes one only if they panic when you are out of sight.
What if I want a little space?
Teach settling on a bed, calmly and rewarded, so being apart becomes an easy skill.
When is following a worry?
Drooling, pacing or crying when you leave the room deserves a professional conversation about separation.
