SENTENCES

 John: "My name's John" (direct speech)

He said (that*) his name was John (reported speech)

(Dijo que su nombre era John)

Se puede observar que después del verbo "said" en el pasado es muy natural seguir con el resto de la frase en el pasado: "...his name WAS John". Esto no significa que ahora John no se llama John, se dice así por razones de una concordancia de tiempos en la frase: "said" y "was".

-       He said that his name IS John

(Dijo que su nombre ES John).  También es correcto.

Consideremos la frase emitida hace una semana:

 Mary: "I'm going to Madrid tomorrow"

Mary said that she WAS going to Madrid the following day  

-       Dave: I HAVE SEEN that film

Dave said that he HAD SEEN that film

-       Mike: I HAD BEEN there

He said that he HAD BEEN there

-       Jenny: I WAS WATCHING a film

    Jenny said that she WAS WATCHING a film. 

    Jenny said that she had been watching a film

-       I'm going tomorrow

He said he was going the next day (o "the following day")

-       I'm playing football next week

He said he was playing football the following week

-       I went last week

He said he had gone the week before

Y si también nos hemos desplazado en el espacio, es decir, ya no estamos en el mismo sitio en el que se dijo la frase original:

-       I like it here

He said that he liked it there

Los verbos modales también tienen su forma pasada que se aplica cuando empleamos el estilo indirecto:

-       I can speak English

He said that he COULD speak English

-       I'll see you next week

She said that she WOULD see him the following week