Copy & Run / How to avoid wp-admin to open up in source ?

Hi, for dev reasons I sometimes need to copy & run a wordpress website, so not to touch any existing files and databases. So I copy the dir and the db, then I change the db settings in the wp-config.php … now I can open up the copy under the domain I assigned it to … only problem is, that if I want to login to the wp-admin, it jumps to the original sites wr-admin, where the copy derived from. Making me believe that there must be another url definition in another file that needs to be updated as well …

Any hint very appreciated.
Regards,
Frank