If you talk about the database name, you can't change it after it's created, you can find all the information here.
If you talk about graph projection, you can't change it after it's created, you can find all the information here.
You can get the name of the current database thanks to an APOC procedure: apoc.monitor.kernel().
Thanks for the responses. As soon as I wrote the question, I got the answer I was looking for. It was the graphName of graph projection that I didn't understand.