Translating when speakers reference themselves by name

This is known as:

illeism: The practice of referring to oneself in the third person.

And while this is not a common practice among native speakers, it is certainly not unheard of. Bob Dole, the republican candidate for president of the United States in 1996 was famous for it.

If something happened along the route and you had to leave your children with Bob Dole or Bill Clinton, I think you would probably leave them with Bob Dole. -Bob Dole

Be aware though that when it is done it is usually done for comic effect because people will take notice and think it strange.

If the author's intent is illeism, translation would need to respect that. If there is no other way of expressing oneself in the native language, then it becomes a matter of style: it would be reasonable to express natural native language in natural English.

Illeism is a rhetorical device in English. Jim's Bob Dole quote illustrates this: Dole was using the third person to refer to himself as though he were someone else comparing the two. Where that's not the intent in the native language, why make it so in English? You will drawing attention to it.

On the other hand, it's also reasonable to preserve the structure of the native language in the English translation, particularly if you are indicating the use of a foreign language or the product of the speaker's self-translation. Hercule Poirot's dialogue is a little odd to native English speakers, for example. Use your judgement you should.¹

1: http://itre.cis.upenn.edu/~myl/languagelog/archives/002173.html