Q. If someone greets me with a “Happy new year” can I respond likewise?

A. Horav Shlomo Miller’s Shlit”a opinion is that it is permitted since in our days there is no religious connotation to the greeting. In addition, you may initiate the salute if it generates a Kidush Hashem by displaying good manners.

Ohalei Yakov (p. 20) quotes in the name the Apter Rov Zt”l, the meaning of the Posuk (Tehilim 87:6) “Hashem counts in the script of the nations” as conveying that during their New Year we are also granted retroactively a better Rosh Hashono judgment. Since the differences between the individual conduct during the two celebrations, becomes now widely apparent and evident, therefore a Good Year salute to anyone is not out of place. (Nitey Gavriel – Chanuka p.418)

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