Where can we get "alias names" for the universe of US companies?

Yes, most companies in our list are in the US, but the majority of them are privately held companies. Does tools like informatica / tibco charge tons of money?

There is definitely a tradeoff between accuracy and efficiency. We are not sure which approach would be better, so want to keep the discussion broad.

In the past, I did fuzzy matching plus a manual selection for smaller lists like a few thousand strings. But for millions of rows, this is just impossible. So we are wondering whether AI-based approaches can help.