The Mishnah states that an alias for a vow has the same status as a vow and an alias for an oath has the same status as an oath. The Sifri (Matos) states that the distinction between a neder, a vow, and a shevuah, an oath, is that one who take a vow is invoking the life of the king, whereas one who takes an oath is invoking the King Himself. The Ran (S.v. ushevuos kishevuos) infers from the Mishnah that one who takes an oath is not required to us the Name of HaShem. Rather, it is sufficient to use the alias term of an oath for the oath to have an effect. Perhaps we can explain this ruling based on the Sifri. When one takes an oath, he is invoking the King Himself, so it is not necessary to use the Name of HaShem when taking an oath.