Surnames and Last names

Why are children always given the initial of their father as their surname and their father's last name as their last name? Even though we say that there is gender equality and blah blah blah. We don't really have it, do we? Because this patriarchal notion is not even questioned, it is followed everywhere blindly to an extent that I don't even know what my grandmother's surname and last name before marriage was. And that brings us to the next issue, why do women have to take their husband's initial as their surname and their husband's last name as their last name? What is the necessity for this? Okay, maybe some might argue that it gives their names a kind of uniformity. But there are other ways to achieve uniformity, aren't there? How about we eradicate the concept of surnames completely and just have last names which are hyphenated. So say the wife's name is Julianna Potter before marriage and the husband's name is Henry Taylor, after their marriage, their names will become Julianna Potter-Taylor and Henry Potter-Taylor or something. There is no one size fits all. Maybe a couple can decide which of their last names is better and they can each go by the chosen name. Or maybe they just keep their own last names as they are, who cares about uniformity anyway? At least, there should be a conversation about this. We cannot by default just expect girls to change their name all of a sudden. And we can't expect that a mother should carry her baby for nine months and no part of the baby's name should even refer to it's mother. The problem is that women themselves do not take women's rights and gender equality seriously. They never think about these things deeply or actively. They don't feel the patriarchy in daily notions. We need to observe our environment very keenly in order to understand it's core. I have a theory about how babies were given their father's initial as their surname, it might be wrong, but it's just a thing I thought. Maybe, in olden civilizations - the cavemen and cavewomen lived in close-knit, small communities. So everyone sees the mother getting pregnant, they see her carrying the child, so they know who the mother is, but they don't know who the father is, so maybe that's how they started calling the baby by his/her own name and his/her father's name, so people know who the father is. For utility it starts and then maybe it just continues and till now we are doing the same thing. So these patriarchal notions which are so small yet so ingrained that we don't even see what is wrong with them, need to change if we want gender equality to be a reality. If we don't make small changes, if we don't think uniquely, we are not going to change our reality. Another issue I see is that after women get married, they are addressed by the title Mrs. and before marriage their title is Ms. But for men, their title is always Mr. Now isn't this patriarchal? These things are small but they have the potential to create huge impact, huge shifts in thought patterns and huge change in the way we act as a society. Some might argue that women have all the opportunities now - we have rights to education, job opportunities, voting, etc. But are we seen as equal? Men still think of themselves to be geniuses in whatever they do and think of women as mediocre. And we women ourselves underestimate our abilities. We are as great as any other man. Even better actually because we don't have the over-confidence that they do. We are humble, honest and we deserve better. Men still dominate most of the leadership positions in our world, most CEOs, presidents, prime ministers, etc. are men. This needs to change. Men are not going to stop the facade that they have built - that they are great. We need to somehow make it known that the facade is a facade and not the reality.