Is this a red flag? (I can give more information if needed)

I am a 19 year old who is going to start her first semester of her sophomore year of college this fall. Last March during the spring semester of my freshman year, my friend introduced me to one of her guy friends, who was an 18 year old freshman. He got my number, and we texted a lot over the next month. At the end of April, we both went to a party and then went back to his dorm room to hook up. The next day he texted me and asked if we could keep hanging out, so we started dating. I am the first girl that he has dated and he is the first guy that I have dated. I like hanging out with him and I am happy dating him, but a week after the night we hooked up he asked me if I would be his girlfriend. I told him that I thought we were moving a bit too fast and that I wasn't ready to exclusively date anyone right now. He told me that he understood and that we could "take things as slowly as I wanted to," but when he went home for summer break he told all of his friends and family about me :horror: All of my friends seem to think that this is normal, that it is great that he wants to commit this early, and/or say that they thought we "already were a couple," but this sets off an alarm in my head. He doesn't seem excessively needy besides trying to tie me down so quickly, but I still wanted to ask.

Is this something I should be concerned about, and how concerned? What other signs should I look for in order to determine if something is wrong and I need to break things off?

Texting a lot, good morning/good night texts, buying you gifts, being overly chivalrous, doing too many over the top favors, calling/texting you multiple times before you respond, crying because you didn't respond quickly, etc. That's needy behavior.

Asking you for a relationship already is needy, and it destroys some attraction. Because really, how well does he actually know you?

Likely most guys your age will be needy.
It's why women go for older men, because they typically are naturally better at this stuff, but even then that's not always true (and no, im not suggesting you date older men).

Random, but funny. If you watch older movies, you will see the men in much more masculine roles.
Like Clint Eastwood, do you see him chasing women and begging to spend time with them? Nope.
Plus, the pre-cellphone days. These guys didn't bond with women through text messages with emojis (haha).
They got to know women through doing fun activities together and by creating great memories. Which is the right way, in my opinion.

I generally don't see anything wrong with telling his friends about you, and the family eh, really it's all to the degree of information that he shared.
If he's saying things like, "I meet the woman of my dreams, shes perfect in every way, I have to lock her down and make her mine".
Yeah, that's a little over the top.

He might have just said, "I went on a really great date with this woman", I still do that.
I just will say a couple sentences about it. "Yeah, she has a really great sense of humor, and dude, when she smiles, f-u-u-u-u-u-u-u-ck".
Without giving really that much detail about it. I always assure my friends/family that its nothing overly serious, and that I have no expectations.
Then we just start talking about other crap for the rest of the night.

Honestly, just do what you want to do. It sounds like you're unsure, so maybe just go with the flow for a while.
I can't tell all of the details, he's likely excited because you're this new woman in his life. Obviously it turned you off a bit though, or else you wouldn't be here posting here.