and now I want to delete the library from my laptop.
Have you checked the copied library, if it is working well in its new location? If not, double click it to open it in iPhoto and browse and edit photos, to check if all is well, before you delete the library on your laptop.
My question is, what happens next time I want to move photos accross to the external? Do they go into the first library or are they saved in a new library?
When you again want to move a photo library to the external by dragging your current photo library there, it will not be merged with your old library there. It will either overwrite it or create a second library.
Also how do you rename a library (so I know which one i'm opening?
Rename the photo library on the external by changing the name in the Finder.
- Select the library in the Finder and press the key combination ⌘I to open the "get Info" panel.
- Disclose the "Name&Extension" brick and enter a new name in the textfield.