Every time a character is thinking something is it necessary to put “_____thought,” if there is italics, so shouldnt they already know that’s what the character was thinking not the narrator speaking?
First, you'd need to establish the convention that you use italics for thoughts. I've seen different books use italics for thoughts, telepathy, foreign-language inserts, and more. The reader would need to know what you use italics for. (See, here I've used italics to stress a word.)
Once you've established the convention, and so long as it's clear who's thinking the thought, (I'm assuming we're only hearing the POV character's thoughts?) you don't need to repeat the "_____ thought" part - it's sufficiently clear without, so reiterating it is redundant.
If you're inside the heads of multiple characters, you'd still need to make clear every time who's doing the thinking. But this can be self-evident from context, just like it is in dialogue.
You merely need to ensure the reader understands who is thinking, and that the text is thought.
"Trevor stood before her, like an ebony sculpture, even more imposing than she remembered. Gods, my father hasn't changed. Morgan thought to herself."
"Trevor stood before her, like an ebony sculpture, even more imposing than she remembered. Gods, my father hasn't changed. The thought sluiced through Morgan's mind.
"Trevor stood before Morgan, erasing her preoccupations. He was an ebony sculpture, even more imposing than she remembered. Gods, my father hasn't changed..."
"Gods, my father hasn't changed... The thought came unbidden as Trevor stood before her; an ebony sculpture, even more imposing than she remembered."
etc, etc, etc
If you establish it as a convention in your novel, no.
Being honest, while there are uses for outright stating thoughts as streams of dialogue-like prose, it's still a very telly form of exposition. Creative narration and use of motifs can bring about the same effect in POV-based narration as outright stating a particular stream of consciousness in italics.
My own convention is to format thoughts much like dialogue, in italics, without the quotes. So I will often start a new paragraph, in italics.
He's trying to trick me.
I will intentionally, early on, add the 'she thought' tag, to establish this convention:
He's trying to trick me, Sandra thought.
I never write to reveal the thoughts of more than one character, so this is seldom necessary, but I still do it once in a while because it sounds right, or especially for linkage:
He's trying to trick me, Sandra thought. "I'm really not interested, okay?"
Because thoughts are often not verbal in any grammatical sense, but a mix of images and feelings and intuition, I will often describe thoughts, that lead to verbatim thoughts:
So that would explain why Mark lied about where the money came from, but why would Allen agree with him? Allen couldn't possibly know what Mark was doing, not back then. Unless he did. Unless he knew all along!
IMO thoughts expressed grammatically are rare, so I would resort to descriptive prose for them most of the time. When there is a voice or sentence in their head, it is usually short, direct and without embellishment, a declaration and not a long description. Often it is a single word: Jerk. To me that is a "believable" thought, and when I want to include it, I treat it as internal dialogue; and use all the rules of dialogue, just in italics instead of quotes.