THEORY: 'to say that...', 'to hope that...'

Hi!

Is there a specific category for verbs like 'to say that...', 'to hope
that...' etc.?

T

"The man who removes a mountain begins by carrying away small stones."
--Chinese proverb

"The status quo sucks."
--George Carlin

"An eye for an eye makes the whole world blind."
--Mahatma Gandhi

"I tried so hard and got so far,
But in the end,
It doesn't even matter,
I had to fall,
To lose it all,
But in the end,
It doesn't even matter."
--In The End, Linkin Park, Hybrid Theory