Can I trademark a word for my brand that is already being used in another brands name of the same industry?
Are you referring to the only word that is registered? (Example, Amul)
If that is the case, although you can apply for registration, you should wisely opt not to. It is likely to see that your application is stuck at the examination stage itself.
However, if you are using only a part of a trademark, there can be fair chances of approval. Example, ABC deodorant. While ABC represents unique prefix and brand value, deodorant is a common noun that no one has exclusive right on.