IANAL, so this is my education opinion only:
Are you offering on 'myexcellence.com' a similar service to what's already offered on 'excellence.com' ? If so, then yeah, I'd avoid the name-clash as they can legally apply to take ownership of the domain name.
If your service is in a completely different market sector, then you should be OK, as there's 1,000s of examples of similar sounding domains but providing very different services.
Random advice from the internet.
Why even waste energy thinking about this?
Just pick something else. Nobody really cares much about the name and if the company is making a pile of money, it can do a rebranding later. For a lot of businesses having something that is easily googlable may help more than having something perfect.
Alternatively, just use the name and move forward building a business. Blatant cases aside, fretting over what might happen because of the name is pretend work. Fretting over the business running out of money is real work.
Good luck.