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.
You could use a significant part of other’s name but not something that truly represents the brand. If you are doing so, it is infringement and unlikely to be registered.
KEY NOTE: In India, prior user gets right over registered one. Hence, if you are claiming prior use and able to prove the same before registry, it is worth fighting for.
Discuss your case with an attorney to find fair view on your case. If you are to register in India, connect with LegalWiz.in