Backup to a network share

I create a dumpdevice:
EXEC master.dbo.sp_addumpdevice @devtype = N'disk', @logicalname = N'Test', @physicalname = N'\\myserver\myshare\myfolder\test.BAK'

I set permisssions, so that a user (mydomain\me) has change permissions to the share and to the folder. (The share permissions are everybody can change).

I start SQL Server Management console, Server Version is 10.0.2531 -> SQL Server 2008. I am logged in to windows and so to the sql server too as \mydomain\me.
Now i fire
backup database mydatabase to Test with format, init

I receive the OS Error 5 (access denied). I add the computers account to the ACL of Myfolder, give the computers account Databaseserver$ change permissions.
Now the backup completes.

What have I to do, that the backup runs not unter the account of the computer, but of mydomain\me? The SQL Server service runs as NT Authority\networkservice, the SQL Server agent (which shall make the backups at the end of the day) runs under a domain user account.

Thanks in advance!
Dresden, Germany