Hindu culture opens doors to spirituality, whose goal is moksha - Self Realization. Ancient saints created concepts in such a way that if one applies them, it brings one closer to self realization. For Self Realization, Renunciation is very important (at least mental). Keeping all ill-practices against women aside, women do not need to take renunciation (I do not say they cannot or do not deserve). The life of women is such that it is very easy for them to progress spiritually.
Hinduism teaches that Karma (action) should be done with the spirit or detachment or acting as an instrument of God or only for God. It teaches to give responsibility to God. The feeling of 'Me' and 'mine' are not good for spiritual progress. This increases or sustains the ego and spirituality is to dissolve ego (sense of individuality) and be merged in totality. So, technically parents do not have right to name their kids. They can take care of kids and give the best they can, educate them, but when time comes, they even need to drop their attachment with kids and other family members, later on even with their own body. This is difficult to understand. It takes time and dedicated study of scriptures and meditate regularly.
In earlier days, new born babies were taken to saints for blessings and saints were requested to give suitable name of baby. Saints with their divine vision (which they get after intense meditation) can see the nature of baby and then used to name baby which suits his/her character. Unfortunately, today, these types of saints are found rare and if found are less active with society.
Even today, where people are not much interested in spirituality and just try to take pride of their religion, or choose to be an atheist, traces of Renunciation are found in day-to-day activities. Kanya-Daan (donation of daughter during marriage) and naam-karan sanskar or naam karan vidhi (naming procedure of child) are to name a few. Unfortunately, it is just followed mechanically, without proper or no understanding. Parents pre-decide the names and mother give it to sister-in-law to include this chosen name in the five options which she will give.
Living with the spirit of detachment is one of the core teachings of Hinduism.
(This is author's reply to a comment on post Women - Spiritual significance and advantage of being female enquiring why parents do not have right to name their baby).