How is the BIMTECH institute related to BITS Pilani, Goa?

Both the college you have mentioned are not directly related. There’s nothing in common besides the brand name that they carry. 

Let’s talk about the institutes one by one.

BIMTECH, Greater Noida:

• The name expands to the Birla Institute of Management Technology (BIMTECH)
• It is located in the heart of Greater Noida.
• It is a postgraduate business school that offers PGDM courses in various specializations

Jayashree Mohta is BIMTECH’s Chairperson & Dr. H. Chaturvedi is known to be BIMTECH’s Director

BITS Pilani, Goa:

• BITS expands to Birla Institute of Technology and Science, Pilani - K. K. Birla Goa Campus. BITS Pilani has around 3-4 campuses, Goa campus is one of them. Also, you would like to know that Pilani is the main college and is located in Rajasthan.
• It is a technical and science institute for higher education that offers the best courses in B. E., M. Sc., M.E., and Doctoral Programmes

Kumar Mangalam Birla is BITS, Pilani’s Chancellor & Raghuram Gunaje is BITS, Pilani’s Director.

Both of them belong to the same BIRLA Family but were started by different people. BITS Pilani was started by St. G.D. Birla. Whereas BIMTECH was started by Late Syt. B.K. Birla (youngest son of Late G.D. Birla. Hence, both the institutes are different and offer different courses.