This is an interesting question.
First of all, a name of a person is his foremost identity. So, when a baby takes birth, parents pour all their love, when they think of a name for their baby. In Indian culture, parents take even extra care while keeping a meaningful name for baby.
Astrology has a big role in Indian culture, especially in Hinduism. Most of the people who follow Hinduism, follow Rashi and Nakshatra for any big incident of their life, such as from marriage to baby birth to keeping baby names to any good occasion. Naming a baby is itself a ceremony called ‘Naamkaran’. It happens on a particular day, again after consulting astrology. So, it is obvious that in Hinduism, parents will keep eye at Rashi and Nakshatra when thinking of a name for baby.
In ancient India, we find many example of name according to Rashi, such as Giridhar(lord Krishna) for Kumbha Rashi(Aquarias), Banbhatt(name of an ancient poet) for Vrishabha Rashi or Taurus etc. Generally, first letter or first two letters are suggested for baby names based on rashi in Vedic Astrology.
Another reason is a scientific one. Psychology says, when you call a person by his name again and again, it influences his personality. Also, according to Astrology, Rashi and Nakshatra at birth time influence baby's future. So, parents try to keep name according to Rashi and Nakshatra hoping that the good influence of her Rashi and Nakshatra might help the baby to build a bright future, when people will call her by that name repeatedly.
In some regions of India, parents keep baby names according to Rashi because such names are indicators of astrological birth detail. This helps keeping track of Rashi and Nakshatra of the baby later in future, without searching it in long document called 'Kundali'.
But, there are many divisions in Hinduism and there are some other beliefs too. In contradiction, some parents do not keep their baby's name according to Rashi. They believe that it may disturb the good stars if anyway people abuse calling that name in life.
Therefore, like the vast and diverse culture, there are many beliefs, thoughts and reasons behind keeping or NOT keeping a baby name according to Rashi in India.
Content credit: Soumi Ghosh