In Gaya, Bihar I came across a common street food there called poached egg/egg poach. A quick googling and some social media discussion made me realize that it is a common english breakfast. The indian version or the Bihari one, rather, uses oil in place of water. The ladle used for this purpose is called 'dabbu'. The inside is often left undercooked and the raw egg oozes out when pierced.
In Kolkata fried eggs [also known as bullseye/ sunny side up] are often called poached eggs.