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 I am not sure what you are asking. I mean this honestly and literally.  There is a way to enter different connection information both in manual (browser) and automated (CLI) restoration. Based on your wording, I am unsure if you are talking about manual restoration through the browser, automatic restoration over CLI, or why the saved database connection information during the manual restoration is not cleared before being presented to you. Please let me reply to all these possible questions.

When you are restoring a backup you are asked to provide the database connection information for each database being restored. The name of the database being restored is shown to you. When you change the database connection information in the restoration page, that's what is used when the database is being restored.

For the main site database the connection information is blanked out in two cases. One, if you have selected not to save that information at backup time. Two, if you are restoring to a different domain, subdomain, or subdirectory – or, at least, if PHP can convey that information correctly to BRS. Note that this applies only to the main site database, not the add-on databases.

When you are doing an automated restoration via CLI you get separate sections for each of the databases as documented in https://www.akeeba.com/documentation/brs/cli-config.html#cli-config-format-database :

The first configured database is the site's main database, and its property name is always site. Every additional database's property name is in the format uniquePrefix-databaseName, e.g. 5118D1DD-example. You can find these names in the installation/sql/databases.json file.

If you meant something different, or need a clarification, please ask me.

Oooh! You mean how the database is defined in the backup profile on the restored site. No, this will never be updated automatically.

There are several practical considerations. To begin with, you may want this information to be updated in some, all, or none of the backup profiles which may or may not have been included in the backup.

Instead of trying to duplicate half of the Akeeba Backup user interface in the restoration script, there's an integration with the Joomla CLI application instead.

Let's say you are using profile 29. To list the database inclusions you'd do this:

$ php cli/joomla.php akeeba:filter:list --type=include --target=db --profile=29

List of Akeeba Backup filters matching your criteria
====================================================

 -------------------------------------- --------- ----------- -------- ------ ---------- ---------- ---------- -------- --------------------
  filter                                 type      host        driver   port   username   password   database   prefix   dumpFile
 -------------------------------------- --------- ----------- -------- ------ ---------- ---------- ---------- -------- --------------------
  C4368DC0-B7B8-40CD-BECA-00F5591BB086   multidb   localhost   mysqli          mydb       foobar     otherdb    bar_     C4368DC0-boot4.sql
 -------------------------------------- --------- ----------- -------- ------ ---------- ---------- ---------- -------- --------------------

You could delete that inclusion with 

$ php cli/joomla.php akeeba:filter:delete --profile=29 --filterType=multidb C4368DC0-B7B8-40CD-BECA-00F5591BB086

And you could define a new one like so:

$ php cli/joomla.php akeeba:filter:include-database --profile=29 --dbdriver=pdomysql \
  --dbusername=mydbuser --dbpassword=mynewdbpassword --dbname=myotherdb --dbprefix='foo_' --check

You could combine that with an automated restoration under the CLI if you are doing that regularly to fully automate the process.