"Why would a woman be considered a "piece of property" by changing her name to that of her husband's"
Because, that's pretty much how the whole concept of a woman changing her name started; back in the good old days when women were, indeed, the property of their spouses.
I figure, do what you want. It just didn't make any sense to me. It just seemed like a tradition whose time had passed. I don't have kids, but I'm friends with five couples who do, and the woman not changing her name was never an issue. Their children are just fine and they are still families in every sense of the word.
I was fortunate that my husband felt exactly as I did. I've talked to women who said that they had big arguments with their husbands-to-be over it, and they went ahead and changed it to appease their husbands. I know it's not the same for everyone, but that would have been a big red flag for me.