Well most English speakers will know Ta-Ta means goodbye.
And probably tities as breasts. But surely if it a big issue then tata should use different name in those countries.
Funny, the third meaning of your link actually is about tata company. Did not know it will go into a dictionary.
I am not talking about cultural sensitivities(thanks for bringing the point though, it is important ), but the fact that chinease sounding names have bad reputation in Indian market.
So as a rule of thumb, if your name sounds like you struck two metals, dont use it as your trucks name. So all names with tong bong etc are out.
TCL is a good example, perfect name, like LG, only you should have quality and service to back it up.