Appelé is by the most used in this context. When you say “my name is” in French, most of the time people will use “je m’appelle”. On this site, you can see that the relative frequency of “appelé” is 40 vs 25 for “nommé”.

Both of your examples are correct. “Nommer” sounds more formal: it is related to the act of giving the name, while “appeler” is related to the name that people use to call you. Also note that you can be more specific when using “nommer”‘s derivative: “prénommer” (first name) or “surnommer” (nick name) can be used.

Nommée sounds more natural in this case.

I would personally not use appelée.

In a more informal way I would use the active voice mentioned by Luke Sawczak :

J’ai rencontré une fille qui s’appelle Amélie.

While I could be off-topic here, if you’re looking for the simplest way to translate:

“In the spring of the year 2014, I met a girl named Amélie”

then I would recommend:

“Au printemps de l’année 2014, j’ai rencontré Amélie.”

The rationale here is that “Amélie” is always a girl’s name so you don’t add any information by explicitly saying “une fille nommée Amélie”.

Appeler is I think used much more than nommer.

The question puts me in mind of the countless riddles in French with what is usually a rather bad play on words involving a first name. They’re quite popular in France, it seems everybody can come up with a few. I don’t know about other French-speaking areas. Anyway, they’re introduced with the set formula :

M. et Mme Machin ont un fils ou une fille, comment le prénomment-ils ou comment la prénomment-ils?

Or,

M. et Mme Machin ont un fils ou une fille, comment s’appelle-t-il ou comment s’appelle-t-elle?

Here are two examples, one basic and one more goofy :

• M. et Mme Térieur ont deux fils, comment les prénomment-ils? Alain et Alex!
• M. et Mme Saintmaloalanagecestpasdelatarte ont un fils, comment le prénomment-ils? Ferdinand!