Do I have to pay for a new iPhone if I have insurance and my issue was a malfunction problem?

If you have Insurance, talk to your Insurance company and see what they say about it. Insurance usually has a "deductible" you need pay when repairing or replacing covered items unless otherwise stipulated in the Insurance contract.

If you mean your iPhone is still under Apple's warranty period (warranty is very very different to insurance) then as long as its determined to be a manufacturing defect, Apple should repair or replace it for free.

You can read the entire Apple Warranty terms here:

Apple One (1) Year Limited Warranty