Do intensive pronouns ever convey new information?

So for instance, the sentence 'I myself am called James' is not different to 'I am called James', information wise.

As a comparative measure, take the sentences, which make use of reflexive pronouns 'I cooked eggs for myself' vs 'I cooked eggs for her'. Here, different information is conveyed, because whilst the object is the same, the subject is different.

But the sentence 'I herself am called James', 'I her am called James', or 'her myself am called Alice', does not make sense, because the object can't be two different things at once.

Note: I've just thought that 'he himself cooked eggs' could imply that only he (whoever he is) cooked eggs, and only him alone. However, I don't think it necessarily means so, where 'he alone cooked eggs', would. Any thoughts on this would be much appreciated.