What is the name of this thorny plant?
Your tree appears to be from the Genus Dichrostachys.

It has several species, quiet a number of them have been reported only in Madagascar.

There are two species found in India, D. santapaui and D. cinerea. 



How have I reached this plant?


The leaves of your plant are bipinnately compound. They gave me the impression of Mimosa pudica. 

Of course it is not one. Mimosa pudica become creepers with time
and have short and thin prickly thorns.
Resemblance of an unknown organism with a known one can indicate shared derived character(s) (Synapomorphy), meaning they can be related. 

Google's algorithm is often able to trace this relation. Look at the keywords I had used. If it doesn't one needs to experiment with the keyworks, note the word Fabaceae, it is the family to which Mimosa belongs.
Wikipedia  often is just the right place to start one's research.

The description of Dichrostachys cinerea is what I checked next, after having ascertained that is found in India.



  Dichrostachys cinerea is a tree characterized by bark on young branches, dark grey-brown fissures on older branches and stems and smooth on the spines.
  
  They typically grow up to 7 metres (23 ft) in height and have strong alternate thorns, generally up to 8 cm (3.1 in) long.
  Flowers of the Dichrostachys cinerea are characteristically in bicoloured cylindrical spikes that resemble Chinese lanterns and are 6–8 cm long and fragrant.
  
  The species tends to grow in rainforest zones.In India, it can occur in dry deciduous forest.



Every thing fits well upto Genus Dichrostachys. 



  Dichrostachys is an Old World genus of legumes in the Fabaceae family. 
  
  Their Acacia-like leaves are bi-pinnately compound. 
  
  Unlike Acacia their thorns are hardened branchlets rather than modified stipules. They are native from Africa to Australasia...


The next thing I exhaustively checked were the species under this
    genus. I checked their
    locations,
    out of all two species have only been reported in India; D.
    santapaui and D. cinerea.

The reason behind this unusual format is to show you  how to fish. I will leave the rest of the hard work of digging up the species to you . 



Few interesting facts about this genus:


Its name is derived from the Greek words dis (two), chroos (colour) and stachys (grain ear or spike), which in combination suggests their bi-colored inflorescences. 





Dichrostachys cinerea, known as Sicklebush, Bell mimosa, Chinese lantern tree or Kalahari Christmas tree (South Africa).
D. cinerea is used in Ayurveda.