Is it appropriate to name your children after relatives who were not Frum? Assuming that the relatives were good people and would fall under the category of "tinok sh'nishba". Would it be better to add an additional name along with the relatives?
From an answer at Jewishanswers.org, I see that
Naming after a relative has two components. The first is according honor to that relative and creating a merit for his soul. The second aspect is that through sharing a name, a ‘spark’ from the deceased’s soul enters the child’s. This can ultimately inspire the child to achieve greatness. For this purpose, the name must be identical to that of the one being named after and it must be the intent at the time of the naming. However, as long as some aspect of the name is preserved in the name of the child, the first objective is achieved and the honor is accorded.
If I understand the answer correctly, it would be appropriate in this case to ensure that only some aspect of the name is preserved in the name of the child.