It's not clear to me from your question whether the court has already signed a final order in your case. If the court HAS signed a final order, then you have to abide by it, including any provisions for name change, possession and access, and designation of competent adults to pickup and watch your child.
However, if the court has NOT signed a final order, then you should hire a private attorney to work with the AG for you. The AG's standard orders contain all the provisions that you asked about in your question. You need a licensed family law attorney to be able to either convince the AG to prospose a different order (they don't have a lot of flexibility on some matters) or argue before the court to get changes.
Here are some comments on your specific issues:
1. JOINT MANAGING CONSERVATORSHIP: The Texas Legislature has instructed judges to appoint both parents as joint managing conservators, unless it would clearly be in the child's best interest to do something else. It is clearly in the child's best interest to do something else when the level of conflict between the parents is so high that they cannot co-parent in any way. That's not the case for most parents. The thing to focus on is not the title of Joint vs. Sole managing conservatorship. The thing to focus on is the allocation of rights and duties.
2. POSSESSION AND ACCESS: The AG's standard order just has a standard possession order built into it. A standard possession order provides that the other parent gets 30 days in the summer. The standard possession order is NOT presumptively in the best interest of a child who is younger than 3 years old. But to get a different order, you have to go make your argument to the court. That takes some experience and skill.
3. NAME CHANGE: The AG's standard order has a name change built in to it. You don't have to agree to it. If dad insists on it, you'll have to go argue before the judge.
4. COMPETENT ADULT: The judge will insist on a provision that says that any competent adult can pickup/return/watch the child. I don't think that phrase includes 16 year olds. But ifyou want to make it clear, take it to the judge and ask that the order clearly spell out that the person has to be 18 years or older with no criminal history. Also, ask the judge for a right of first refusal so that you can watch the child when dad is gone during his periods of possession for extended periods of time.
The AG seems coercive and like they are in charge, but they are really only acting as a mediator who is looking out for the State of Texas. The AG cannot force you to agree to anything. If you and dad can't agree to something, you have to take it to the judge.
I am very famliar with the courts in Dallas County and can assure you that the family law judges there will do there best to look out for your baby's best interests. But if you don't have theexperience or knowledge to make the proper arguments on issues that you want to contest, you may have a very hard time because the judge has to treat you the same as a licensed attorney and can't give you any advice or even any hints.
Name change? No, he cannot force you to change the child's name. Person's picking up/dropping off: it depends on what your papers state but usually it limits to age 18 and over. If your child is 7 months old, you can petition the court for modification of visitation to where he has no overnights until child is 3 years old. This isn't in the Family Code any longer but it's still preferred by judge's. Court's prefer the parties be joint managing conservators unless there are other factor's that make it unsafe or otherwise not in the child's best interest for the father to have equal rights with you. i.e., drug usage, noninvolvement, etc... You should speak to an aggressive and experienced family law attorney who handles child custody modifications.