Being a mother you should put emphasis for the right of choosing the name for your baby yourself, although it is not a religious obligation or any social compulsion. Still it can make the process of naming the baby less complicated.
The father of the baby has as much right for naming his baby as the mother and either of them can be a rightful candidate to choose name of the baby. This will reduce level of the competition and in fact the task is done there and then, without any delay and feedback from other members of the two families.
You as a parent can allow any member of the family to exercise their choice and right to name the baby but do not let the competition take a stiff turn that other people take it as a matter of honour for them. Sometimes, some relatives of the child can get angry for not being asked at the time of naming the baby.
You can ask for the contribution or opinion and then can decide the name yourself. This can simplify the process and might make everyone happy. Even if the name they choose is not selected they will be satisfied on getting the honour of presenting their valuable opinion.
One way is to chose the family name or sir name that is generally in fact all the time is associated with the father's family name, and then you can choose the first and middle name at your convenience. The first name can be a choice of one person and middle name of another person. Sometimes middle name is also decided with the father's name so the matter is left only to the first name.
It is sometimes better to let the grandparents decide the child's name. Generally they have more love and feel for their grandchildren than other members of the two families and they get a sense of happiness to have chosen the name of their grandchild. This can also make you feel good. Sometimes, paternal uncles are the keen parties to name the baby, who can be given a chance provided the parents and grandparents are indecisive about naming the baby on their own.