Ah, what a cool question! I know, it's such a strange name, right? And Tonks herself clearly doesn't feel it fits her, given that she goes by Tonks instead.

I think the best I can do is that I do tend to think of Andromeda as a bit traditional - not in a prejudiced pureblood way, but just, she grew up in this very traditional, formal family, and my take on Andromeda is that she still retains some of that in her personality - very upright posture, very erudite vocabulary, fiercely smart and with a lot of inner strength, maybe even comes across as a bit imposing to those who don't know her. (Seems like the impression we get of her in her one canon scene, that for a moment she seems a little "haughty" and almost looks like Bellatrix.) Opposite to Ted who I imagine being incredibly down to Earth and cuddly and warm, really close and easygoing with his daughter. (To be clear, I think of them both as amazing, supportive parents who do everything in their power to make sure their daughter grows up happy and well-adjusted, after the prejudice Andromeda and Ted had to live through to be together. Just, two amazing parents with two incredibly different personalities!)

So I can kind of imagine Andromeda choosing an ornate, old-fashioned name for her daughter, even though she's broken with tradition in so many other ways. I have Ted always calling Tonks by a nickname, and Andromeda always calling her by her full first name, and Tonks putting up with it only because it's her mum. :-)

(Another long answer to a short question, sorry!)