You could create a custom dialplan hook. It would extract the display name from the calling channel. If it began with a +, it would set the outbound caller ID accordingly. See
However, what you are asking seems very strange, because you would need to change account settings whenever you wanted a different caller ID. If you are making calls on behalf of two or more persons, departments or organizations, there are much easier ways to handle it. The two most common are having an extension for each (you select the appropriate account before calling), or having a dial prefix for each (you dial the appropriate digit before the called number).
If neither of the above meet your requirements, please describe your application in more detail.