He told her that he loved her > He said her, "I love you"

[Hansman]

He told her that he loved her. (indirect speech)
-> He said to her, "I love you". (direct speech)
I have learned that the first sentence as an indirect speech can be converted into second sentence as a direct speech.

He said that his name was Sam. (indirect speech?)
-> He said, "My name is Sam". (direct speech)
Can I think that the first sentence is also an indirect speech and can be inverted into the second sentence?

 

[Tarheel]

"He said that his name was Sam" is indirect speech.

Say:

Is the first sentence also indirect speech?

 

[Skrej]

He told her that he loved her. (indirect speech)
-> He said to her, "I love you". (direct speech)
I have learned that the first sentence as an indirect speech can be converted into second sentence as a direct speech.

That's essentially correct. It's less common to use the 'say to' pattern with direct speech, but it's not incorrect.

He said that his name was Sam. (indirect speech?)
-> He said, "My name is Sam". (direct speech)
Can I think that the first sentence is also an indirect speech and can be inverted into the second sentence.?

Yes, that's correct.

Here are a few broad guidelines for direct and indirect (also called 'reported' ) speech:

Reported/indirect speech:

• Use 'say' or 'tell' (in past tense)
• Don't use 'say' or 'tell' to talk about reported questions - you must use another verb such as 'ask' (in past tense)

Direct speech

• Use 'say' (in past tense)
• Use 'tell' (in past tense) only for instructions/commands or information
• Use 'say' (in past tense) for direct questions, but don't use 'tell' for direct questions.

Finally, remember that when using 'tell', you need a direct object.