Is there a name for the words used after dialogue?

Question

For example, "he said" "she replied" "they inquired."

Answer 1

They are usually called speech tags by writers.

Answer 2

In functional grammar, they're known as projecting clauses.

Answer 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.

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Toolan, M (1998) Language in Literature: An Introduction to Stylistics, Hodder Education

Answer 4

Speech tags is commonly used by writers, as given already, and often abbreviated to just tags, though like many short terms it only makes sense if you know the fuller form.

Those other than the simpler said and asked are often called Swifties or Tom Swifites or said-bookisms.

The first two because the "Tom Swift" series of children's adventure books were written by someone who was so afraid of the repetition of said that he would go to great lengths to avoid it, and so came up with a great variety of other tags, which made the tag stand out more than the dialogue most of the time.

The last because you could once buy "said books" that provided near-synonyms of said and adverbs that could be applied to said, just so that you too could turn perfectly good dialogue into writing that jarred and buckled under the reader's eye like a snake having a epileptic fit.

Swifty is also applied to a game where you deliberately produce such pointless tags, but with a pun too ("It's freezing," he muttered icily).