You're using PG's code in a trademarked/copyrighted environment (the domain is called exactly HackerNews). That's blatant copyright infringement, you should have gotten YC's permission before, not after the site went live. What you have done is illegal in both US and India.
You should respect the law and change the name or take the site offline until you receive appropriate permissions.
Please note that even licenses as GPL or MPL (that govern the Firefox code for example) give you permission to use the code, not the trademarks of the project. Ubuntu had to make a Linux package called "abrowser" ( https://launchpad.net/ubuntu/lucid/+package/abrowser ) simply because Mozilla didn't agree with branding their modifications as "Firefox".
I may be wrong, but "Hacker News" does not appear to be trademarked in the US. And the code is open source. So which particular laws are being broken here?
the existence or non-existence of a trademark registration filed with the USPTO doesn't necessarily mean that the name is trademarked or not. registration helps when you're suing, but trademark rights can attach without registration.
Why do you keep repeating "not for profit". As some have already mentioned, ( http://news.ycombinator.com/item?id=1913237 ) it does not make brand name abuse anymore acceptable. Financial profit is not the only thing, there are issues of "social profit" as well, and those have to be earned too.
Make no mistakes, I agree that its a great service. I would use it myself if the outstanding issues are resolved. But as I have said before, helping yourself to someone else's brand and work isn't very ethical regardless of its legal status. My views about that wont change even if pg agrees out of politeness.
Copyright, IP and trademark don't only apply when profit is involved.
I reserve judgement on the appropriateness of appropriating the Hacker News name---but please don't labor under the impression that you can use someone elses (c)/(r) as long as you aren't making money.
Aside from seeking permission---you really should add a footer stating you are not affiliated with Y Combinator etc etc.
Hacker News, as far as I can tell, belongs to Y Combinator, which is a Limited Liability Company, not a non-profit. It may be something of a loss-leader, but it does belong to a company.
Why don't you just make a sub-reddit for this? If there is really such a huge demand for this, people will go there. That way you can focus on really trying to solve a problem for Indian hackers and avoid latching on to the HN brand.
I won't comment on copyright infringement or anything of that nature.
However, I thought I might point out the irony of all of this. A "decent" definition of Hacker is "a programmer who breaks into computer systems in order to steal or change or destroy information as a form of cyber-terrorism" (http://wordnetweb.princeton.edu/perl/webwn?s=hacker).
The irony comes when hackers get mad at other hackers hacking their hack.
I also plan to launch reddit india. If someone complains I will try to look for the owners to check if they have any problems.
NOTE: reddit india will be not-for-profit
Create a website this week called Google India. Make the UI look about the same as Google.com, but with a little different color scheme. Then send an email to Google's founders asking if it's okay. That's similar to what you're doing with HN India. :)
The situation is not exactly the same, because you did start with a code snapshot that PG made available to the public. However, it's generally considered bad form -- as well as confusing to visitors and search engines -- if you use a name that is extremely close to the original site's name.
Things would be different if you created something in a totally different medium, or if, as others have pointed out here, you first got explicit permission from PG and YC to do this. The site name "Hacker News", though it is composed of two generic English words, does now form a unique reference to a specific site that carries a certain cultural cachet and set of expectations. To "ride" that, without permission, is not a good idea, even if you can get away with it.
One good thing that may come of this, however, is the notion that perhaps there's enough demand to make PG consider adding a "sub-Reddit" like feature to the HN codebase. So folks like you who basically just want to not reinvent the feature set, and also want to address an approximate subset of the core HN readership -- where in this case the subset is Indians or India-ophiles, etc. -- could do so freely with explicit support and functionality that enables it.
A point that I would like to make is that HN is non profit and so is HNI. So the analogy you give may not apply here.