I recently started a brand-name based website, not a generic-keyword-base website. I am finding it hard to market it since it's kind of a new word. Needless to say, I'm not much getting organic traffic yet. Is link building with keywords anchor text and social media the only way for now ?
you need to promote website whether it has keyword or not in its domain name. promoting a newly created brand is a different story.
People associate a level of quality with a brand. Create a high quality site (design wise), loads fast, with high quality content that has value and your brand will grow. There is no point in branding a low quality site.
use the brand keyword along with targeted keyword to help, but it will take time to get the brand noticed in the SERPS
I agree with evanlambda that people will associate level of quality with your brand, and hence work on the quality of your website. However content is as important in your case. Yous should work on expalining the meaning and purpose around your 'new word' and like binaryqwest says, use it along with targeted keyword to help your brand get noticed. For that you should probably work with adwords and some targeted keywords to generate interest and curiosity towards your site. Using social media for now and in the long run is also a good idea.
Yes you should work on explaining the meaning and purpose of your new word. Then people will be able to understand your brand name along with its usage. Because in your case you are using brand name as key word.