Thank you for taking the time to help.
My question is with respect to store bought challah bread. Sometimes on the bag it is written “Shomer Shabbat.” How should one dispose of this bag? Does it require geniza? Is Shabbat one of G-d’s name’s and therefore this would be considered sacred?
There are authorities that say that one should not say the word Shabbos in the bathroom etc., which would mean not to throw it out. However, most poskim are lenient and the minhag is not to be strict with this and you may throw it out.
See Sharei Teshuva O:CH 84-2 in the name of Birkas Yosef, Pischei Teshuva Y:D 176-28 who cites Radvaz that the minhag is not to be strict with this that since the person does not mean H-shem when saying or writing the word Shabbos. We also see that the minhag is to write the word Shabbos regularly without leaving out any letters, as is done when writing H-shem’s name. Also see Ginzei Hakodesh chap. 7 ftnt. 21 citing see Ben Ish Chai 1 Vayetzei, that is strict in this regard, however see see Sdei Chemed brought in Gnizei Hakodesh that this is only for the very pious. Poskim