Echo's messaging feature uses contacts to pair phone numbers with the name of the person in the contact list you tell Alexa. It will then use that phone number to identify the Alexa user. So remember to provide Amazon your phone number during the installation process.
Everything will work normally unless you forget to update your contact information. For example, if you send a message to your mother's Echo Dot, you will have to save the "Mother" name in the directory, using the correct phone number that she uses for the Alexa account.
Make sure the person you are calling is also using Echo. This feature will work when both of you follow the steps above.
Here are some notes.
If you don't have an Echo device in your hand, hurry up to the nearest store and experience this amazing smart speaker product.