Does the mother's name affect one's luck, scientifically and in terms of health, and to what extent do names influence our lives?

The meaning of the name's effect on luck is not clear. If the question is about the psychological effect of parents' names on their children, then this is not unlikely, as names have a psychological effect on their bearers, both positive and negative. That is why the Prophet, peace and blessings be upon him, clarified that the most beloved names to Allah are "Abdullah" and "Abdul Rahman", and he changed bad names to good ones. The effect that occurs on individuals due to their names is not unlikely to occur to them due to their parents' names.

However, if the intention is the effect of the name on a person's destiny and what is decreed for them in life, then that only happens by Allah's will and decree, and the goodness or badness of a name alone has no effect on that.