I will answer you as nobody else will. Hacker News users are interested in this idea, but don't want to divulge their actual address to get a "price quote". Ideally, they'd like to give their zip code and get a round-about dollar figure they can use to compare to their current pricing.
Fair enough. The reason we ask for your name first is because we want to create a more personal chat experience. We believe that buying insurance should not only be instant but also delightful.
The comment above yours clearly states HN users don't want to divulge exact address. In fact, they specified their ideal (zip code->quote) but you start justifying why you ask for name when nobody pointed as that being the issue.
To be fair, every other major renters insurance company requires a lot of personal information up-front before giving you a quote. I don't see why this should be different.
Do you use name and address solely to be delightful or do you use it in other ways, like to order insurance score, clue or prefill any other 3rd party data for additional segmentation?
If it's simply checking one credit agency, you could let the user enter in a credit score from whatever credit agency you use to get a quote, but let the quote be contingent on their credit score exactly matching that.
"The reason we ask for your name first is because we want to create a more personal chat experience."
When I'm doing a research online before buying something, I really don't want "personal chat experience" with every dozen of companies which website I check. If I would -- add a phone number, Skype etc. in your contacts and I will call myself. Companies, that do not provide clear pricing, usually don't even make to my primary comparison table.