Is it wrong to think that naming a newborn with a certain name will make their characteristics similar to those of other people who bear the same name, and does this fall under the forbidden practice of Tatayyur (superstitious belief in omens)?

This way of thinking is incorrect. As long as the name is good, it should not be changed merely because another bad person bears the same name. The Prophet, peace and blessings be upon him, did not command those whose names resembled the names of polytheists to change them. Rather, names were changed based on their meaning, such as changing the name "Barrah" due to the connotation of self-praise it carried. Nevertheless, there is no harm in changing a name to another good name, and this is not considered a bad omen.