How can I ask a respondent for their name and then use it in following questions?

Probably not needed, but here's an example:

Q1: Hi, what's your name?

A1: Luke

Q2: Ok, nice to meet you Luke! Where are you from?

A2: [...]

You can pass an input field's value to a field label using the field's UNIQUE NAME.

Related guide: How-to-Find-Field-IDs-and-Names

Once you have the field's unique name, use that within the label of the question where you want it to populate and enclose it with curly braces {uniqueName}.

In the example above, the full name field's unique name is hiWhats so it was placed as {hiWhats} on the next question.

Ok, nice to meet you {hiWhats} Where are you from?

Here's a sample form showing this behavior: https://www.jotform.com/80976101343958

Thank you!