Are women's names being changed in those of their husbands to show the world who owns them?

Surnames are a relatively modern invention, began in Northern Europe, and in many countries outside of Europe and the British-colonized lands the wife does not take the husband's surname. Since a married woman's place in society was essentially determined by the position of her husband, and she was the premiere member of the household of which he was the front-man and public face, it was natural that she would be known to strangers as the wife of (Mrs.) So-in-So, and not by the name of a father in whose house she no longer lived, and who was most likely dead already. When her husband died, her position in society was likewise largely determined by her eldest son's, who inherited his father's surname. Even so, in many parts of Europe (Scandinavia, Russia, etc.) patronimics (So-n-sos-SON) were the norm for all until about 50 years ago, when standard family surnames were finally adopted just so every family didn't require 3 seperate entries in the phone book (one for the father's patronimic, one for the wife's patronimic, and one for the children's patronimic).

In certain Latin American countries the wife typically adds the husband's surname to the end of her name with the adjective "de" (of) in front of it: e.g., Eva Duarte became (officially) Eva Duarte de Peron when she married Juan Peron.

In none of the cultures where the woman took the husband's surname was it about showing "ownership" - at no time in European or American history has a wife been the property of her husband. (You can legally destroy or abandon your property: you couldn't legally destroy or abandon your wife.) Indeed, it is in the cultures where women have the least standing and least rights and are little more than a special class of chattel that they don't take their husband's family name.

Ancient Rome also had both clan names and a kind of surname, but the wife never took her husband's: in fact, whereas Roman men had (typically) three names - the personal name, the clan name, and the surname/nickname - women only had one name which was her clan name, and all the women of the same clan had the same name: Gaius Julius Caesar's paternal aunts were both named Julia, his two sisters were named Julia, and his daughter was named Julia. (The younger daughter typically had a diminuitive suffix added: e.g., Julilla = little Julia.) As clans had dozens to hundreds and even thousands of families, if it was necessary to be more specific as to which Julia, Claudia, or Antonia one meant, their father's surname was added but as a patronimic, not an actual surname: e.g., Caesar's daughter was not Julia Caesar but Julia Caesari - literally, Julia of Caesar. It was never thought that any woman was ever so significant as to require more of an identifier: a woman's place was in the home, so why would anyone outside that home have any need to refer to her?