What is difference between I2C and TWI?
I agree with everything @Wouter said... Namely, TWI is used by manufacturers (like Atmel) to refer to their I2C interface to avoid legal trouble with Philips since I2C is a registered trademark. Some manufacturers (like Atmel) have implemented proprietary features on top of I2C so that their TWI is an I2C superset.

To answer your follow-up question, yes. It is enough just to change the name. A trademark only protects the name. If it were patented, the situation would be different. 

However, it is difficult to defend a patent on a modulation/encoding scheme since it is mostly just math. Often, copyright is used for this, but it is usually pretty easy to circumvent, since the copyright protects only the exact specific instantiation (implementation) of the protocol, not the protocol itself in most cases.