Q. Re- last questions Someone that davens nusach Ashkenaz-Sefard (Chasidish) is he obligated to answer Omain after Mekadeish Shmoi Berabim, when there is no mention of Hashem’s name?
If he is not obligated, is he allowed to answer Omain at the conclusion of that bracha? How about Boruch Sheptaruni that people recite without the Shem?

A. As mentioned in prior question Shulchan Aruch (O.H. 215: 2) rules that one is obligated to answer omein after hearing a brocho. However Poskim rule that this incumbency is limited to a brocho that contains at least one of Hashem’s names.
Shaarei Efraim (4: 25) rules that in places where the bar-mitzva blessing of baruch sheptarani is said without mentioning Hashem’s name, omein is usually omitted, although it could still be said.
So it would seem from the fact that one answers omein at the end of birchas hazimun after the meals (Shulchan Aruch O.H. 198: 1) or after the chorachamons of birchas hamozon.
Betzel Hachochmo (5: 89 and 90) differentiates between brochos. The ones that were established from the onset to be recited with Hashem’s name, if the name was omitted there is no point in saying omein although it is still permitted. The above applies also to doubtful brochos where Hashem’s name is omitted. Another category would be brochos that were constituted to be recited without Hashem’s name, on these one should answer omein after them.
Horav Shlomo Miller’s Shlit’a opinion is similar, he added that one may answer omein to these brochos as one should after hearing any blessing. brocho or tefila said by or to an individual.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a