Baby’s name and hospital visit

Do I have a right to ask everyone who takes photos of my son when he arrives not to blast his last name all over social media? Do I also have the right to say who can come see me while I’m at the hospital?? Ugh my mom wants everyone to come see my son and I while I’m at the hospital but all my family does is take shit about everything and i really don’t want them there... Also his last name is my moms maiden name as my pos father doesn’t deserve to have a grandchild under his last name at all and I don’t want the baby to have his fathers last name as we aren’t together and let’s just leave it as complicated af and the father is alright with his son not carrying his last name!! I just don’t want to be snappy towards my mom but feel I have a right to say who i want to come see my son at the hospital and who he is around... also feel I have a right to ask people not to post his name all over social media... Do i have the right or am I just begin selfish ?