Q. What is the correct way to salute a newly converted Ger that one encounters after the immersion in the mikva? Does one have to say Shalom Aleichem? Does one have to recite Shecheyanu?
A. Maseches Gerim (1) mentions that after the tevila we entreat and encourage the ger with words of blessing and inspiration, such as: Fortunate are you that merited to join the Creator of the Universe and to join the ones called His children. (Birkei Yosef Y.D 268).
The new name is given after the immersion and usually a Mi Sheberach is also recited. There are different traditions and nuschaos as to the tefilos that are then said (See Igrois Moshe Y.D. 1: 161: 162 – Madrich Lager p. 85, Dinei Hagiyur Vehager).
Horav Shlomo Miller’s Shlit’a opinion is that one does not need to greet with Shalom Aleichem and should not recite shecheyanu when encountering the newly converted, but may bless them and say mazal tov.
Horav Moishe M. Lowy Shlit’a added that one has a mitzvah to greet the convert beahava, with love.  Say Mazel Tov and give them a big welcome to Klal Yisroel for becoming part of the Am Hashem.  
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a