One daughter, Emma Gwendoline.
We looked through books and talked about them. Surprisingly few of the names grabbed either of us. For a daughter, my wife wanted a name ending in -ine (four of the women in her immediate family are Corrine, Adeline, Nadine, Sandrine), and we both liked the sound of that one. My wife has also always had a fondness for the name Emma, which has good connotations for her from various literature (Jane Austen, Emma Bovary, and of course Emma Peel), and that also jived well with my family's series of unusual female E-names (Edris, Elva, and a couple of others farther back).
So we had two names we liked, and we didn't decide what order to put them in until we met her. It's a good thing she turned out to be a girl, because we never came to an agreement for a boy's name.
So to sum up, we both liked the idea of having a name that followed a family phonetic pattern, rather like the lines of kings in Tolkien's appendices.

But we also looked at the meanings of the names, what the nicknames would likely be, and so on. Emma had the advantage of being short enough that it probably wouldn't get nicknamed.
Dunno if we'll ever have a second. One is already more than a handful! Some couples get the easygoing, calm baby first, but that wasn't our luck. Emma is as strong-willed as all her namesakes rolled into one! She's lucky she's cute, that's all I'm saying.
Ben