How are the words Amy and Amelia written in Gallifreyan?
I found something like that, but I'm not able to verify its correctness.
This will be the name of my daughter, so this will be printed on the wall
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There is no canonical Circular Gallifreyan. However, you are not totally out of luck. In 2011 a fan by the name of Loren Sherman created a system that has been used by the show on official merchandise including a comic.
Gallifreyan is the fictional language of the Time Lords, from the TV show Doctor Who. On the show, it's usually just random circles. I'm not affiliated with Doctor Who or the BBC, but back in 2011, I created a "Gallifreyan" writing system. It somehow got really popular among fans and eventually made its way onto the show.
His system is based on the Gallifreyan depicted in the show. But would not be able to decode any of the Gallifreyan shown.
All forms of Gallifreyan [...] are based off of Gallifreyan in the show Doctor Who. They're fan made however, because the Gallifreyan in the show cannot be decoded because there is simply nothing to decode.
Omniglot | Sherman's Gallifreyan
What does the Gallifreyan in this episode translate to?
Nothing, unfortunately. In Doctor Who, they just draw random cool-looking circles for Gallifreyan.
A Guide to the Gallifreyan Alphabet - Loren Sherman
Using this, your first image is close to what the translator outputs for "Amy". But here are both.