I would take all of specialmom's advice to heart, and also limit his screen time, research has shown that television before age 2 is a real issue for kids due to its impact on brain development.
Hi there and welcome. Well, some of what you mention is absolutely normal three year old stuff and some is more concerning. Kids of three do tend to want to be with their parents so his following you around is age appropriate and what most 3 year olds do at home. I would try to have something that my boys hadn't done in a while ready to go---- and would give them that so I would have 10 to 15 minutes max that they'd sit and do whatever it is that I gave him. I had a bag of magnets for example (all sorts of neat ones, letters, numbers, train ones, sesame street characters, etc.) that I would give him to play with at the refrigerator while I started dinner. he only got to do it when I was making dinner so when they came out, he'd be excited (should say they as I did this with both of my sons). I'd have certain toys that I put up and would get out and then they'd be excited and play for a bit with that item. So, put some toys up and get them out only when you need to do something and you will have a couple of minutes of peace to get started.
Tantrums are absolutely normal for that age and you describe a boy that has difficulty with speech so you will see a lot of this. Hard to convey anger,m frustration, sadness when you have no words to use for it. I would read books on emotions with him to give him language. I'd say "oh, you look mad. What can we do?" And then have things he can do to help release the anger appropriately. Pushing his hands together, taking a deep breath, have him use paint and put handprints on a piece of paper that you tape to the wall and these are his helping hands that he then can go press against when upset (very soothing/calming), and ultimately, using his words will be helpful.
Sharing and kids of 3 is often not great. You work on this. ALL kids are works in progress so just work on it. I would have some one on one play dates at your home and work on this specifically. You can do a 'trade' rule. If someone wants something that another has, then they have to trade so that everyone has a toy. And special toys can be put in his room so he knows that sure, some specific few special things don't have to be shared but all else is to be enjoyed by everyone. AND, make him share his toys with YOU. You treat him like he is a peer at home and make him use the trade rule with you and share his toys.
Now, you do mention things that I think you need to evaluate him for. His speech is not where it should be for his age. And you mention that he might not know his name? He CAN respond to commands or instructions, right? (which is good). I'd talk to your pediatrician about that. His speech doesn't sound 'too' far off though in that he is communicating with you. But if you are around other three year olds and it feels way off, get it checked out. My son had a speech eval. at 3.5 years old. He ended up being within normal but it was peace of mind to find that out.
As to not listening to adults, I would set boundaries. Talk about it when alone with him ---- WE RESPECT ADULTS. And when he doesn't, pick him up and leave. If it is at daycare or preschool that this is happening, they need to give him a time out or whatever consequence they give right then and there when he disobeys or is disrespectful. I wouldn't expect him to socialize with adults of chit chat. You can work on that but this is harder for some kids. I have one who is quite charming to adults and another that barely makes eye contact and we work on it. Same mom, but different kids.
I'd also give him lots of physical outlets. Take him outside and have him run, jump, climb, slide, skip, roll, etc. good luck!!