Is there a name for the words used after dialogue?
Solution 1:
They are usually called speech tags by writers.
Solution 2:
In functional grammar, they're known as projecting clauses.
Solution 3:
Toolan (1998:106) refers to them as matrix clause or framing clause; he gives the examples of:
She said, 'I'm sorry I can't stop right now.'
and
She wondered why those types always picked out her to ask.
The second example is of course reported or indirect speech, but the same principle applies.
Toolan, M (1998) Language in Literature: An Introduction to Stylistics, Hodder Education