Zemirot - Repeating God's Name
It is a tremendous mitzva to sing the traditional Shabbat zemirot at each of the Shabbat meals. Many individuals choose to sing the Shabbat zemirot in their full form, complete with the name of God wherever it appears. This includes zemirot whose traditional tunes result in repeating God's name numerous times in immediate succession. For example, in the Shabbat Zemer "Baruch El Elyon" the common tune has one repeating the word "La'el" in the refrain "Hashomer Shabbat Haben Im Habat La'el Yeratzu K'minchat Al Machvat" three to four times. There are, however, those who feel that repeating God's name in this manner is unacceptable. According to this approach one substitutes God's name with "Hashem" wherever it appears. Others recite God's name the first time it appears in a passage while using "Hashem" when repeating God's name in the same passage.
It appears that the opposition to repeating God's name in the zemirot likely originates from a halacha found in the laws of Birkat Hamazon. The Rema rules that in the event that one omitted "Ya'ale V'yavo" in its proper place in the Birkat Hamazon, it is not to be inserted at any other point, for fear of using God's name in vain. Similarly, repeating God's name as part of a refrain in the zemirot or in a manner which deviates from the original wording might also be a misuse of God's name. In addition, we are taught that whenever one says God's name one should do so with a feeling of awe and reverence, even trembling. As such, it can be argued that singing God's name in the course of a song and other casual contexts should be frowned upon.
Addressing the concern of the Rema, the Magen Avraham questions what he clearly considers to be an obscure ruling. He says that we regularly recite prayers using God's name at various points in the liturgy without any concern that doing so may be in vain. He further states that it is only when using God's name in the course of a blessing, to the exclusion of a prayer or praise, is there ever a concern of using His name in vain.
(Based on this Magen Avraham, among other findings, I don’t believe that the issue of repeating God's name in Zemirot is related to the issue of Chazzanim repeating words in the davening or the famous "Modim, Modim" discussion of the Talmud. However, this is an issue beyond the scope of this chapter).
The Biur Halacha seems to agree with the Magen Avraham's approach, although he offers his own explanation as to why the Rema might have considered inserting a missed "Ya'ale V'yavo" into the Birkat Hamazon an exception to the general rule that one is permitted to use God's name freely in prayers.
As such, it seems that those who choose to sing the Shabbat Zemirot complete with God's name, even if it means repeating it within the context of the tune, are completely entitled to do so. In fact, Rabbi Shlomo Aviner reports that it was the practice of Rabbi Shlomo Zalman Auerbach to repeat God's name in the course of singing zemirot. On the other hand, most authorities, including Rabbi Betzalel Stern, maintain that one should not repeat God's name when singing zemirot even though doing so is essentially permissible.
Make no mistake, even according to those authorities who permit one to repeat God's name in the course of zemirot insist that one's intention when doing so be in order to praise Him and not merely to fit His name into the tune!
 Zohar, Ekev, p. 272; Shir Hashirim Rabba 8:19.
 Rema, OC 188:7.
 Chayei Adam 5:1; Kaf Hachaim, OC 5:1
 O.C. 188:11
 Maharam Schik O.C. 31
 Although I personally oppose the repetition of words in davening, it is not clear that doing so is completely forbidden. Aruch Hashulchan O.C. 338:8
 Berachot 33b
 Biur Halacha 188 s.v. "v'ayn l'omro levatala"
 Rivevot Ephraim 8:39; Aseh Lecha Rav 7:9.
 B'tzel Hachachma 4:52; Yabia Omer 6:7, 7:14.
 For further study on the issue of repeating God's name in the course of prayers, songs, and the like, see Piskei Teshuvot 215:18; Yabia Omer 6:7, 7:14. See also Nefesh Harav p. 160.