It emerges from the Mishnah (Nedarim 9a) that just as there is a concept of a “yad”, or a “handle”, for a neder, where a phrase can effective suggest a neder without expressing the entire verbal formula, a “yad” is effective in creating a sh’vuah as well. The rambam’s codification of this is surprising: he records this ruling in the laws of Nedarim (1:26) (as well as recording in the laws of Nezirut that a ‎”yad” is effective for nezirut) but does not mention the concept in the laws of Sh’vuot. R. Ya’akov Betzalel Zolty (Mishnat Ya’avetz, Yoreh Deah, 13:4) explains that according to the Rambam, there are essentially two sets of rules that pertain to sh’vuot. One the one hand, there are the rule of “sh’vuat bitui”, which carry with it a korban and malkot. Those require G-d’s Name, and require full expression. For these purposes, a “yad” is not sufficient. On the other hand, there is another standard, one that represents a prohibition of “bal yacheil”, requiring adherence to the commitment. In this case, a sh’vuah is grouped with a neder, and thus works with the same rules: G-d’s Name is not necessary, and a “yad” is effective.