What happens to creatures on your person when you Wild Shape?

Question

If you choose to have your equipment meld with you and you are carrying a puppy in your backpack does the puppy meld along with your stuff or does it get kicked out?

If it melds with you and you decided to turn into a giant Frog since it's part of your body and form does it breath the same as you underwater or is it drowned when come back up after an hour?

Answer 1

The rules are intentionally silent, so you have options

The 5e does not have strict rules for this particular situation. It's a game about battles, heroes and monster slayers, not about pet carriers abusing their pets. The general rule for all corner cases — it's up to the DM to decide. The game developers suggest to "go with what's best for your story":

What happens when someone swallows a druid in a Tiny form? Is a druid fecund in beast form? The rules are intentionally silent on these corner cases, leaving adjudication to DMs. As always, I say go with what's best for your story.

If you are the player, ask your DM. If you are the DM, choose one from the four possible outcomes and stick to this ruling for the rest of the game:

1. The puppy is meld. That means it was a part of equipment, which I guess was not the way people run their games, but styles differ
2. The puppy is not meld, but the backpack is. That means the puppy is magically "ejected".
3. The whole backpack is not meld.
4. You cannot wild shape with the equipment meld, until a creature is inside it. A more restrictive option than 3.

Answer 2

The creature either falls or clings to your new form

Per the PHB, p. 67:

You choose whether your equipment falls to the ground in your space, merges into your new form, or is worn by it.

No mention is made about creatures. It wouldn't make any sense if they were absorded into your body. It's definetely safe to assume they aren't directly affected by your shapechanging at all.

If your hawk pet is standing on your shoulder, it either stays firm on your "new" one, or it is forced into flying (or fall in a... Hawkward manner), depending on what beast you transform into. If you are carrying a puppy in your backpack, the backpack is absorbed into your new form and the puppy most likely falls on the ground. You can't suddenly transform while shaking hands with someone and having their hand fused with yours. You can burn it if you transform into a Fire Elemental, though. The creature suffers the indirect effect of being in contact with your body while it changes shape, but it doesn't get involved in your transformation.