It says in all the seforim (e.g. Orach Chayim 124:5) that one says "Baruch hu u'varuch shemo." But some people say "Baruch Shemo" instead. Is either one correct halachically, or only the former?
@cookieson03. The author of the Torah Temimah, Harav Baruch Epstein zl, in his Sefer Boruch She'omar on tfillah (page 114, this part of the sefer not available on hebrewbooks.org) writes that he was told that many people stopped saying "Baruch hu varuch shemo" as its gematriya is 814 which is the same as the gematriya of "Shabtai Zvi" and his followers ardently undertook to mention it to commemorate him. He points out that this gematriya is only true without the "vav" of "uvaruch" and advises to make sure to say it with the "vav". I once heard that this might be the source of people saying "Baruch Shemo".
Rabbi Lieberman writes
"It is brought in the tur in the name of his father the "Rosh"= Rabbeinu Asher who explains the reason for saying Baruch hu u’varuch Shemo is in response to the saying the name of Hashem as expressed in the Passuk (Devarim 32:3) When I call out Hasem's name praise God for his greatness". (See Tur and Shulchan Aruch 124) The Kabbalists also attributed great importance saying to Baruch hu u’varuch Shemo correctly. (כף החיים סי' ה ס"ק יב.) Unfortunately as you said many people say it incorrectly because of the way they have it heard it from others. When you think of it, it's one of the few parts of prayer which everyone knows you are supposed to say it, but it most siddurim it is just not printed. So people without giving much thought to what they are saying continue to say it the incorrect way and some others swallow their words since they are not used to speaking in Hebrew.
It would seem baruch hu u'baruch shemo is the correct form, and any deviation - like baruch shmo - should be changed.