Why don't I have the option to change the sender of the survey in the invitation composer?

Usually, this is because your user profile has all necessary permissions to send survey invitations but does not have the access right "Can edit company details".

To send a survey with a colleague as a sender, you need the access right "Can edit company details".

Otherwise, the invite will automatically come from you and that button will not be available in your invitation composer:

More on access rights at this link.