Name is a String property that represents the persons name in the Email address. 

Updating the Name or Address portions of the email address causes the Text property to be updated to reflect the new email address. 

For example: 

   // var AEmail: TIdEmailAddressItem;

   AEmail.Text := '"John Doe" <jdoe@some.net>';
   // AEmail.Name contains 'John Doe'
   // AEmail.Address contains 'jdoe@some.net'
   // AEmail.User contains 'jdoe'
   // AEmail.Domain contains 'some.net'

   AEmail.Name := 'Jane Doe';
   AEmail.Address := 'janed@another.net';
   // AEmail.Text contains '"Jane Doe" <janed@another.net>'

Use Text to access the concatenated Name and Address for the email address. 

Use User and Domain to access the mailbox and registered organization for the email address.

TIdEMailAddressItem.Text 

TIdEMailAddressItem.Address 

TIdEmailAddressItem.User 

TIdEMailAddressItem.Domain