“Centennial Anniversary” is actually putting two nouns together. It would suffice to just say “Centennial”. Using the word Anniversary behind it is probably redundant. It is understood in the word Centennial, which is defined as a 100 year anniversary.

I don’t hear or see the word Centenary used that much. I’d bet a lot of people might not even know what it means.

Everybody’s heard “We are celebrating our Centennial this year.”

Your example sentence doesn’t sound quite right to me with either form; ‘beginning’ hits me incorrectly. Sounds like you’re trying to say you are just starting the first 100 years of a business, instead of commemorating the 100 years that just passed.

I would change that sentence to read

“Our business is commemorating its Centennial this year.” Unless you had some other totally different concept in mind.