The privacy is a myth, if you want to actually use the cryptocurrency to pay for things in the real world. If you pay fiat to get monero, the exchange has your info. If you cash out monero for fiat to buy something, the exchange has your info. The wallet and transaction in chain are permanent in the ledger. So where is the privacy?
Unlike with BTC with Monero you can’t tell what I did with the coins in between the two fiat transactions. For most people that’s a very meaningful level of privacy, even if it’s not perfect.
Monero has some limited form of privacy that's fairly good in practice: you can't determine which of N accounts is the origin of a transaction, where N is some fixed small number (6 in Monero I believe).
I don't mind the company I'm buying an item from to know my name and where I live to send it to me. I do mind if they have the ability to look up my address balance or past transactions to other entities.
Atomic swap from Bitcoin is the easiest and most effective choice. If not that or a local, in person swap, the worst they know about you is that you owned Monero at some point. This is assuming you take the required Op-sec for your level or paranoia.