The Rama (OC 188:7) writes that even though one who forgot to recite “Al Hanissim” during bentching should recite “Al Hanissim” in the Harachaman section of bentching, if one forgot Yaaleh V’Yavo on Rosh Chodesh the custom is not to do so. Rama explains that since Yaaleh V’Yavo contains the name of Hashem, saying this tefilah when there is no obligation might be considered reciting Hashem's name l’vatala (in vain). The Magen Avrohom (188:11) questions the ruling of the Rama. We recite various tachanunim (prayers with requests) and include the name of Hashem. Why is Yaaleh V’Yavo different?
The Biur Halacha (ibid) and Aruch Hashulchan (OC 188:17) respond that saying Yaaleh V’Yavo to fulfill an obligation and not as a voluntary tefilah, is treated more stringently. Nontheless, Rav Yosef Dov Soloveitchik (following the custom of his father, Rav Moshe), did not recite G-d’s name when singing Shabbos zemiros, based on the position of the Rama regarding Yaaleh V’Yavo (Nefesh Harav, page 160).
