Meinstest Du Dictionary: evolving ?

He is still building character. 

Adolescents are still building character 

(kein English Native Speaker)

to develop character?

Es ging mir nicht so um das Wort Charakter, sondern die generelle Entwicklung einer Persönlichkeit. Man sagt doch z.B. "Na, der entwickelt sich noch. " oder "Sie entwickelt sich prächtig, seitdem sie in der neuen Abteilung angefangen hat."

So was in der Art. Ohne das Wort Charakter im Satz, obwohl man das meint.

I object!

The use of "evolve"/"evolution" isn't limited to only the biological/genetic change in the Darwinian sense. See above. (M-W also lists "evolve" and "develop" as synonyms, but as high-school students soon learn after they've been encouraged to use a thesaurus by their English teachers, just because words are synonyms doesn't mean that they are always interchangeable.)

However, in this case, I'd go for develop/development as well.