Q. Is it okay to name a child after both his paternal and maternal grandfathers? (Double name comprised of one of each grandfather, neither grandfather had a double name.)
If not, is it okay to change the name after the child has become an adult?

A. There is a disagreement between Poiskim if a name created by joining two names of two separate individuals constitutes a new name or is it still two separate names.
Ben Ish Chai (Shoiftim 27) Sdei Ha’aretz (3 22) Zecher Dovid (1: 84) Zoicher Habris (11) and others maintain that it is proper to give the combined names of the father and the father in law to the newborn and it honors both. This they claim is the indicated procedure to follow in cases where sholom bais is at risk. (See also Yam Shel Shlomo on Gittin 4: 26 on the name Shneiur and Keser Shem Tov p. 96)

However, Machane Chaim (E. H. 43), Chazon Ish quoted in Avney Yoshfei (O.H. 196: 3), Horav Yaakov Kamenetzki Zt”l quoted by Horav Dovid Pam Shlit’a and others, maintain, that combining two names creates an entirely new name that does not have a correlation to the two originating names. This is similar to the addition of a new name to the ill that is generally considered as a name change. (See also Keser Shem Tov ibid. an Otzar Habbris ch. 6).

Horav Shlomo Miller’s Shlit”a opinion is that although this is considered a new name, it still is an honor to the late forefathers since part of a name or even a single letter can be attributed to their remembrance and benefit, analogous to the yud of Sarah’s previous name, being allocated to Yehoshua’s new name. (Sotah 34b, Bamidbor Rabboh 47: 1). Also in people’s perception it is considered a tribute and a sign of respect.

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