- add an option to subscribe to updates or newsletter - auto-generate 10 interesting domains and send them out.
- add an option to watch domains based on a combination of words, subscribe by email
- add an option to search domains based on an industry: Health, Security, Consumer, Photo, etc... - I can share more how it can be done
- add an option to support a project - donate button.
- I would probably a/b test for moving save|buy buttons next to domain, it was not clear for me that I can buy
- would be nice to have some help with synonyms and meanings of the words, should help to non-english speaking users.
Overall, I love the project, so far it has best UX compared to others I used. The challenge with your business model - people don't need to buy domain right away, but they might put your service in a bookmark and return after a while, so:
1) first marketing it a couple of more months, to grow the total number of such users.
2) I'll probably not use namecheap, and go with another registrator - can you add more options here and make money on other referral program?
3) you can add a referal link to more services, such as Launch a Landing Page
Except Product Hunt - there is beta list, indie hackers and many forums, quora and etc - and as some said, you can capitalize on blogging, twitting about successful Launch on Product Hunt, as well as do 2nd launch with major upgrades.