After connecting to a different DB, the Browser lets you know that the DB has been switched but it doesn't tell you the DB name that was connected to.
Connection updated
Your have switched connection.
It would be nice to know, as the Browser results is a like a log of what you did. (I believe you can get the current DB name, but that's an extra step that you have to remember to do and may not anticipate that you wish you had done so.)
Actually.... I do find myself confused. If I do SHOW DATABASES I don't see movies anywhere. I'm not sure how to see that movies is the active DB. I do see that neo4j is a database, so I'm confused as the difference between neo4j and movies. (I may have asked about this before but I have since forgotten about it...)
Whenever you're using browser, the DB you're connected to is shown in the prompt. See the screenshot below, where the mouse cursor is.
If you only see a $ sign, that means you're still connecting. Otherwise you'll see the name of the database you're connected to here, so when you reconnect - it's the same and a separate notification shouldn't be needed.
What I see in this screenshot you've shared is that you have a Neo4j Desktop project called poc, containing 1 Neo4j DBMS (also named poc). By default, a Neo4j DBMS contains 2 or more databases ("neo4j", and "system"). The name of the DBMS in desktop is not the same as the database name in browser.
As a result, I think the prompt saying "neo4j" is correct (you're connected to the neo4j database in the DBMS called poc)