Dont't know if it is really a problem of Multi Sites.
When I like to generate a new site, I enter the name "localhost" at the line "New DB Server name". At the submission it records the server IP adress instead of the expression "localhost" into the DB. That's not really wrong but the DB works only with the expression "localhost".
So, to get it running I have to change it manually.

I am not able to reproduce it.
Can you give a detailled scenario.

Where do you get the "localhost" converted into an IP address.
Is this in the JMS Template definition that you get an IP address after that you have entered "localhost" ?
Is it in the JMS Manage Site definition that you get the IP address ?
Is it in the Joomla "configuration.php" that you get the IP address ?

Which are the version of Joomla and JMS Multisite ?

It's a thing that generaly occurs when I submit the dates I entered previously in the mask under "New DB Server name:". For Example in the template mask. After the dates are submited into the Data Base the expression "localhost" ist converted into the IP adress of the server. So, the dedicated Host for the database and the user permissions get the Server IP instead of localhost. And that doesn't work.

I uses Joomla version 1.5.22 and Mulit Sites Version 1.2.46

I don't see any dates field into the template detail.
Can you give a screenshot of the template that you defined and surround the dates field.

Here it is. That's the mask when you are creating a new site from a template.

This is not the "template" screen but the "manage sites" detail screen.
It seems that you are using a rule that I can not really read.
Can you give the screenshot of the "template" rule that you selected in the "template" field.

I will try reproducing it but it but for the moment it seems that in your "template" rule, there is almost nothing. No DB parameters. Perhaps you just have selected the master DB but I don't see it.