My mother does not remember her Jewish name and always uses the literal- hebrew translation.
Should I just set this as her name (when using my name, son of, for a request); do I need to make a name change at shul, or formalities, to be official?
If a name was desired to be added, not typically used, formal procedure would be required (she has a vague recollection a certain name could be hers, so it could be combined).
Thank you for your question.
The first way to verify this would be to check her kesuba. However, if that is not available, then since the translated name is the name that she uses, that would be her name. For example, if she is called Rose, then you can use the name Reuvain ben Rose. If she wants to add a name to herself, then it would only count if there are people that will indeed call her by this name.