Depending on how you are triggering the send, you have two main possibilities:
If you're triggering the send from the REST API, you'll be using this endpoint. In this case, as you can see from the documentation, you can set both the
From.Name and the
From.address. This overrides that of the Sender profile which you may have selected.
On the other hand, if you're using a different method, it get's tricker. The easiest way, in my opinion, is to set up the Sender profile with AMPScript. I'll explain it below.
Setting up dynamic Sender Profiles with AMPScript
First you want to setup a data extension with the following configuration:
In that Data Extension, you will populate all the Sender Profiles you need. One row per sender profile.
Once you have that setup, you will create a brand new Sender Profile and in both in the name and the email you will insert the following script:
%%=lookup("DataExtensionName","FromName", "Id", AttributeValue("senderProfileId"))=%%
%%=lookup("DataExtensionName","FromAddress", "Id", AttributeValue("senderProfileId"))=%%
Now, just reference that Sender Profile in your Triggered send and you should be set :)