The architect of the Ram Temple being constructed at Ayodhya is Chandrakant Sompura. It is important to note that the Sompura family has a long legacy in temple architecture and has been involved in the construction of various temples across India.

Option 1 - P. O. Sompura: This option is incorrect as there is no architect named P. O. Sompura associated with the Ram Temple project.

Option 3 - Brinda Somaya: This option is also incorrect as Brinda Somaya is a renowned architect, but not involved in the construction of the Ram Temple.

Option 4 - B. V. Doshi: This option is also incorrect as B. V. Doshi is a renowned architect and the winner of the prestigious Pritzker Architecture Prize, but he is not involved in the construction of the Ram Temple.

Therefore, the correct answer is option 2 - Chandrakant Sompura, who is the architect of the Ram Temple being constructed at Ayodhya.