What should Xinbei be called? Call it Shuangho (雙河). This would be Twin Rivers in English, giving it a pleasant, pastoral sounding name representing the Danshui and Keelung Rivers that flow through it. In Chinese it would have not only the two rivers(河), but also the two "ho-s", Yungho (永和) and Chungho (中和), and thus be a nifty play on words.
New North City is lame. New Taipei City is ok but boring. Your suggestion?
[Taiwan] Don't miss the comments below! And check out my blog and its sidebars for events, links to previous posts and picture posts, and scores of links to other Taiwan blogs and forums! Delenda est, baby.