I needed something like this literally last night, glad to find it now.
If you want it to be more widely used, maybe it could use some SEO or marketing love? You don't seem to be on page 1 for company name generator, business name generator, name generator, etc., and you deserve to be. Get an h1 tag, get a few blogs to list you on their "top 5 web 2.0 name generators" articles.
Thanks, the kind words mean a lot. To be honest, I am not sure why the website has done so poorly in terms of search, but that is a good idea to reach out and try/get it on some top lists of web 2.0 name generators.
1. This is 2016 and I don't know what are you doing without ANY social media presence (at least, none that is visible on the site)? With the kind of service that you have there, LinkedIn and Twitter should work well. Insomuch as social signals is one of the SEO factors today, this would help SEO to some extent as well
2. Consider creating a blog section on the site and publishing relevant posts periodically
3. How about creating a widget/plug-in type functionality using which other sites can copy-paste some code to display a box saying something like: Generate a Great Company/Product/Domain Name, with the basic input features of your app and a Generate button and then, when users hit the button, they reach your site where the results/name suggestions are shown? With something like this, I am reasonably sure you should be able to interest at least some domain registrars and hosting companies to bite!!
HTH. I'll be happy to volunteer further/hands-on promotion/SEO/SMO work in case you're interested - let me know, and all the best.
If you want it to be more widely used, maybe it could use some SEO or marketing love? You don't seem to be on page 1 for company name generator, business name generator, name generator, etc., and you deserve to be. Get an h1 tag, get a few blogs to list you on their "top 5 web 2.0 name generators" articles.