1. The Company Law,1956 does not deal with the names of the companies. THE EMBLEMS AND NAMES (PREVENTION OF IMPROPER USE) ACT, 1950 of GOI restricts certain names to be used by establishments. Besides, the name of a new company is verified by the Registrar of Companies that it should not be very similar or suggestive of an existing company.
2. The company using the word "International" does not mean that it is serving many clients in different countries. It would be suggestive of that its subsidiaries and branches are incorporated in many countries. A multinational company.
3. If nobody has patented the word "International" in India, you can use the word in India. But if you start operating in some other country where the word International has already been patented, you may face problems. The same happened with Jet Airways when it started its operation in US where already a small company called Jet Air or something that was already operating.
Thats why, very common words like India, National, American, British, Nippon,International, Intercontinental etc. are at best to be avoided.
To my mind, apart from Patent regime, there is no law as such which bars the use of the word "International".