If I read it carefully, the Catholic Encyclopedia does not state anything about the point of time, when
Saul received his second name
Paul. Of course I have no idea what Deissmann had (!) to say about this (the articles on the site are almost 100 years old). And unfortunately I can't find my source any more telling that
Paul could have possibly adopted the name
Paul altogether as an adult. But I don't think this really matters. The connection with "strutting" was new to me, though. Thanks!