There are a couple of ways to do this depending on how you are building your application. This answer is assuming you are building both forms as a multi-page form within CognitoForms.
Say you have a form consisting of a single field "Name" on the form. Now you add a page break so that you have a second page where you want to collect more information such as email and address.
Add a second field "Name" here and on the settings click on the "Default Value" field. In that default value field, enter an "=" sign and then you can select the Name filed from page 1 from a dropdown.
So at this point, the customer enters their name on page 1, clicks next, and on page 2 sees their name already filled out along with the additional fields such as email and address.
If you are actually using two different forms, it's a bit more complicated but you can pre-fill the fields with the query parameter - see here.