What are written name conventions in labels?
It would hang on the door to celebrate the name of the new baby. It could also hang on the wall; it's more of a decoration than an indicator


The key word is 'decoration'. You can consider it a hand crafted art. The shape of the sign should be fun and artistic (e.g. you can make it shaped like panda, star, duckling, bunny or anything you consider meaningful ). It can also be colorful. The same goes to the font you use. 

Horizontal or vertical are both fine, the characters don't even have to be the same size or line up straight, but the label itself should has little thickness to make it feel substantial

Use just the baby's first name would make it more casual and relax. Using full name would make it more formal.