I'm sorry, I'm not understanding. Take a look at this article:
In it, it states you must specify the source and destination server. You would just use the instance names; so source;ServerA and Destination:ServerB. Are you not able to connect to them over the network?
I would install SSMS on my desktop computer; make sure it's from the latest version you are using (like SQL 2014). You should be able to connect via SSMS to both ServerA and ServerB.
To use the Copy Database Wizard, you must specify the following:
The source server where the databases to be copied reside.
The destination server to which the databases are to be copied or moved.
The databases to be moved or copied.
The name of a target database, if different than the name of the source database.
The source database name can be use for the copied or moved database only if name conflicts do not exist on the destination server. If name conflicts exist, you must resolve them manually on the destination server before you can use the source database name there.
Other objects to be copied or moved; for example, logins, shared objects from the master database, jobs and maintenance plans, and user-defined error messages.
The schedule for the copy or move operation, if you want it to run at a later time.
If you are not a system administrator, you must specify a SQL Server Agent Proxy account that has access to the Integration Services (SSIS) Package execution subsystem.