Naming a child after non-observant grandparents

If someone’s deceased grandparent was not Torah observant, but financially enabled his children to have a Torah education and was a mentsch, can one name a child after him or her?

The prohibition is against naming a son for a "rasha" - an evil person about whom Shlomo Hamelech wrote (Proverbs 10 7) "May the name of the wicked rot" (see Yoma 38b and Rashi there). The person you describe in all likelihood would not fit this category and in his generation's social context is most probably a "tinok shenisbah"- someone with an inadequate Jewish education who was not taught properly an appreciation of Jewish observance. Shu"t Yehuda Yaaleh I 199 mentions that it is permitted to give a child the name even of an evil-doer (and again- it does not seem that the grandparent falls into this category) if it was also the name of others who were not evil doers.