Here the word "name" refers to God, himself. To forget God is to stop worshiping him. This is something that did not happen. Alternate translation: "If we had forgotten our God" or "If we had stopped worshiping our God" (See: [[rc://en/ta/man/translate/figs-metonymy]] and [[rc://en/ta/man/translate/figs-hypo]])
Spreading out the hands is a gesture that people used to worship and pray to a god. Alternate translation: "worshiped a strange god" or "prayed to a strange god" (See: [[rc://en/ta/man/translate/translate-symaction]])