Is one allowed to say Hashem's name when singing Zemirot?

Gabrielle Hiller asks: What is the root of the controversy with saying Hashem's name or not when singing zemirot on Shabbat?
This is a very practical question that comes up virtually every 7 days!
The root of the contraversy is centered around a Gemara in Masechet Sanhedrin 101a which states, "If one reads a verse of Shir ha'Shirim as if it was a song (i.e. unlike the proper cantillation), or reads verses in the Beis ha'Mishteh (pub) out of place (just for fun), he brings evil to the world; The Torah girds itself in sackcloth and complains to Hash-m 'Yisrael treat me like a harp for Letzim to play'!"
Rabbi Howard Jachter has a good summary of the issues involved in his book Gray Matter, Vol. 3., page 7 (it's a short article).