Syncing, Importing and naming a database

I am not sure this is a new topic, but I didn’t find anything and I don’t want to mess this up:
I created a database on my MacBook 1 and at home I want to import it (so I have it on MacBook 2). If I import it via CloudKit, it asks me to NAME the database. When I just keep the name, it tells me it will overwrite (which I don’t want to do). So I give it another name - is this database now in my iCloud twice? Is it on my MacBook (or BOTH MacBooks) twice? Does it sync?

So basically, can/need I rename the Database when I import without loosing all the syncing and without wasting immense hard disk space?

Does this mean that there are two databases having the same name? Or that you created a database on computer A and another database on computer B having the same names?

Welcome @polemikus

You had to have created or copied a database the the same filename already.
If the database had been previoisly imported via syncing, DEVONthink would just open that database when you tried to import it.
If you import the database you would need to rename it to avoid overwriting the file, but no this would not sync with any other database, regardless of what name you gave it.

As far as I remember, I wanted to import the database which was on MacBook (MB) 1. When i clicked on the import icon on MB 2, it opened the „save to“ dialogue. When I just agreed to save it, it told me that it could overwrite or I had to give it a new name.

Do I miss something? Or did I do something wrong sonewhere?

Did you use Migration Assistant or Time Machine to set up the new Mac?