If so what traffic sources should I use? Facebook ads? Google adwords? I read Tim Ferris used google adwords to test the title of his book. But I know now you cannot use it anymore. What can you use instead?
Use the "Link Text" in your facebook ads to A/B test various domain names.
To do this, simply launch a few identical ads, and only change the link text to say the variation of the domain name you are considering.
The ad with the highest CTR (not conversion rate or other KPI) will be the one that sparks the most interest in your target audience.
Note: one domain may have a high relevance to one audience, but low relevance with another. So this tactic should only be used if you have a very specific demo you are targeting.