How can I use existing email addresses and data (names, last names etc.) to display the person's name when they visit my WordPress website?

The first and most important step is to remove the anonymity for the visitors. This can be done via

• Send them an email, have them click a link in an email that goes to the website
• Phone you via a dni replaced number on the website
• fill out a form 
• have them type their email address during an olark chat

Once the anonymity is removed, all future visits you can auto fill forms, display their names in dynamic blocks etc.

You can use the dynamic blocks to accelerate the anonymity removal. You can use referring host, pages visited, keyword searches, keyword search before ad clicks, etc, to start shifting the dynamic data on the website. 

The book a meeting popup and book a meeting link on our website uses our integrated meeting scheduler. This works extremely well for removing anonymity. It is less a 'please give me your name' then a 'you should give your name as we need to know who we are meeting'. 

This is a good video to watch

https://www.youtube.com/watch?v=8X25Tggbs9g