With the example you gave, it is okay to drop the 'that'. Reason being,
It is far easier for the reader to infer 'that' has been dropped when you have co-subject material in both main and that clause (like in yours: She yelled she), e.g.,
You said you loved me v you said that you loved me
With yours:
She yelled she had some names v she yelled that she she had some name
I have to admit that second is better on the ear, but I think that's more down to the choice of verb:
She said she had more names v She yelled she had more names
Said seems to work better without 'that' than yelled, but that is just my personal choice here.
She yelled that she had some names.
You can also drop 'that' when they aren't co-subject
She said I could go (She said that I could go)
Other instances where 'that' is seen to be retained:
Passive voice: She was informed that he had died
When there's a noun between verb and that-clause: she warned him that he could die
that-clauses (as coordinator): The impeding danger to both sides is that one... two... etc
When there's paranetheicla material: Perhaps we should assume, all things considered, that this isn't going to go away.
