To begin with, think of having three aliases in the database server. You can see them using SQL Server Manager Configuration tool.
The technique is to use Export/Import option of the system registry. Be cautious and do not try to modify other things. All the keys of the SQL Server aliases can be found for a x64 system in the following path:
And whether you have SQL Server 32-bit on x64 then the keys are found here:
Now, once the path was found we need to navigate to it and right click on it to select Export option to export the branch of aliases to a regedit file (.reg). Finally, copy the file to the new server and then using File->Import option you can import them into the registry of the new database server. That is all for now. Let me know any remarks you may have.