Cracker - because she's been 'pond' after her marriage all the way through, and they made a big point of it around melody's birth (she's 'river song' because it's a translation of 'melody pond'). It is possible this is all a cunning ruse and deliberate use of 'williams' to show we're somewhere else in the timestream. But to me it just seemed like crappy writing.
Back in the day, a woman took a man's last names to symbolize that she had ceased to be part of her dad's family (and his property with his label on), and had become her husband's property, with his label on. Obviously, lots of women still take their husband's names for reasons that aren't so clear-cut, because it's become fairly normal in our society. But:
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Amy has elsewhere said quite clearly she doesn't like Williams and prefers Pond (for Melody/River).
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The Dr uses 'Williams' when he's saying she has to grow up and stop being an adoring child in her relationship with him. He's telling her to sever her relationship with him, and to symbolize that he gives her her husband's name, as if passing her into Rory's care and as if (for Amy) being married is how she becomes 'grown up'.
When you think about it, it is pretty rude that marriage is seen as a way of recognizing Amy as a proper grown up.
I have ishoos with this because my dad, when I got married last year, told me very firmly that he saw it as me becoming properly adult. I told him how offensive I found that (ffs, I'm older than my DH and have earned my own living and had my own home for years ... what is it about me marrying Dh that makes me grown up?), but he didn't get it.