Can information collected in JotForm be updated....like a database of names and addresses?

If I collect names, addresses and phone numbers using a jotform survey, is there a way to have respondents update the information that they had submitted previously. 

Yes, there is a way for your respondents to edit their submissions. Just setup an email AUTORESPONDER and include an EDIT link on the email so your visitors/respondents can edit their submission as they see fit.

Here's the complete guide on how to achieve that How-to-Let-Users-Update-Their-Form-Submissions-at-a-Later-Date 

Now, I noticed you mentioned "like a database of names and addresses". Although this is somewhat different from your aim, just in case you're interested in knowing how to push submissions to your own Database using MySQL, here's how:

1. First you need to enable your form to post data to a custom thank you page URL How-to-Post-Submission-Data-to-Thank-You-Page 

2. Once that's done, use this page as a guide on how to setup your database to receive your submission data How-to-send-Submissions-to-Your-MySQL-Database-Using-PHP You might need to have a developer set this up for you.

Nonetheless, if your only aim is to let your users edit their submissions, then the first part of my reply would suffice.

Hope that helped!