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Primarily because it is an administrative headache (not an impossible task, just another painful task for people who are already overburdened)- and the people there (inside IITB) don't care as much about the issue as the people from the political parties that want the name to be changed. They really do want to do better and more productive things than to pander to the whimsical desires of politicians on this name-change brouhaha.
Either way, it isn't IIT Bombay's prerogative to change its name to whatever it wants. Considering the legal status of the IITs, any change of name has to take place through an act of Parliament as an amendment to the IITs Act[1]. There was some talk about an amendment back in 2008[2], but nobody really knows (or cares) about what happened of it.
Interestingly, IIT Bombay is not the only entity to not have been renamed. The Bombay Stock Exchange and heck, even the Bombay High Court have not been renamed. Over in Chennai, IIT Madras retains its old name.

Yes, with a Diploma in Mechanical Engineering, you may be eligible for lateral entry admission to the second year of the B.Tech. in Aeronautical Engineering program at Annasaheb Dange College of Engineering and Technology in Maharashtra.
However, admission criteria may vary depending on the college's policy and may be subject to change. It is recommended that you check the official website of the college or contact their admission office for the latest information on eligibility criteria, admission process, and fees for lateral entry admission to the B.Tech. in Aeronautical Engineering program.
In general, to be eligible for lateral entry admission to the B.Tech. in Aeronautical Engineering program, you should have completed a three-year Diploma in Mechanical Engineering or an equivalent discipline from a recognized institute with a minimum aggregate score of 60%.
Once you meet the eligibility criteria, you can apply for lateral entry admission to the B.Tech. in Aeronautical Engineering program through the college's admission process, which may involve an entrance exam, counseling, and document verification.
Annasaheb Dange College of Engineering and Technology is a well-regarded engineering college in Maharashtra that offers a range of undergraduate and postgraduate programs in various engineering disciplines, including Aeronautical Engineering.

There are opportunities in R&D as well as other corporate jobs like patent and market analysis.
1. R&D: There are some entry-level jobs for freshers in Biotech firms. Job responsibilities may vary from QC (Quality Checking), sales (as this requires basic technical understanding also), data analysis, technical support etc. As graduates are not that sound in technical skills, they are not involved in hard-core research. Salaries and perks are obviously not that great at this level. To be honest, such jobs are good only if you wish to pursue higher studies in future (Masters and/or Ph.D. sometime soon. For the time being, you can get in and learn some skills.
2. Patent/ market research: yes, you can get into KPOs (Knowledge Process Outsourcing) firms, where you get to combine your Biotech/ Life Sciences background with and/or to provide solutions to your clients (which would be Biotech/ Pharma/ Food Tech firms, mostly) and help them take strategic business decisions. But then again, such firms also expect sound technical knowledge and thus mostly hire at least Masters level guys. You can start here at junior designations and can make decent money. Not bad if you want to gain work experience for a couple of years.

Yea, it is a college. The Cluster Innovation Centre has been designed to seek and drive innovations from industrial clusters, village clusters, slum clusters and educational clusters. It strive to stream relevant ideas and programmes stemming from the above mandate into its learning and research programmes. The CIC has pioneered the concept of a Meta College as well as a Meta University and runs highly innovative state of the art learning and research programmes. It provides following courses:
B.Tech. (Information Technology & Mathematical Innovations)
B.A. Honours (Humanities & Social Sciences)
M.Sc Resources and Information. (Mathematics Education) @ Meta University.