What exactly are Hakafos Shniyos (practiced on Motzai Simchas Torah in some communities) and why is this not considered KiNireh KeBal Tossif especially if HaShem’s name is pronounced during the singing? Why would this be any different than sitting (and eating) in the Sukkah on 2nd day Shmini Atzeres if the person had in mind (not LeShem Sukkah), but simply LeShem Simchas Yom Tov or LeShem Oneg? Thank You.
The minhag of dancing Hakafos Shneios comes from the Arizal, the same person who instituted the minhag of doing hakafos on simchas torah based on the Zohar. Actuality he said that there should be dancing with the torah four times, the night of simchas torah, by day, by mincha and after maariv the night after. The reason for this is based on Kabalah. Most communities however only do the first two hakafos. There is no Bal Tosef since it is only a minhag and the minhag is meant to be this way. When a person sits in the succah and the torah said only to do it until the 21 day of the month and he is sitting there longer then it can look like baal tosef.
The fact that Hashem’s name is mentioned is not a problem because we are allowed to say his name whenever we are learning or praising Him.
Shar Hakavanos pg 104, Kaf Hachaim 669-30