Can SSIS packages call other SSIS packages in the connection string?
The connection string is not calling another SSIS Package. The property Application Name is optional filler text so you can differentiate one connection from another.
Application Name=SSIS-&lt;Transfer-Now-name of other SSIS package&gt;-{8ABA18EE-637E-424F-A3F7-F7E4EA50DD9D}&lt;IP.db_name.user&gt;

If Transfer-Go has the a reference to Transfer-Now in the connection string, the probable cause is that the developer created Transfer-Now and then copy/pasted either the package in whole or at least the Connection Manager between the packages.
The mechanisms for one package to run another package are

Execute Package Task {either as an in-process (synchronous) or out of process (asynchronous)}
Execute SQL Task
Execute Process Task

The later two options will have you either running a predefined Agent Job or building out the appropriate commands to dtexec