And it's also been upheld that private businesses have a lot of power in deciding how/who they allow shopping, hiring or workers, and participating in society.

Religious and 1st amendment leeway to discriminate goes both ways.

What are those names?

There are dozens. Right to privacy is one example. It’s not in the constitution but supported by the Supreme Court’s interpretation of the law. These decisions build on each other. For example, the right to an abortion is built on the right to privacy.

No, they aren't. Those are privileges.

Shopping is a privilege granted to those who have money, which isn't a right.

Working is a privilege granted to those who have skills the market is willing to pay for, which isn't a right.

Participation in society is preconditioned on obeying the law, and can be taken away through arrest and imprisonment.

“Privileges” aren’t a legal concept. You have the right to bear arms in the US, but that doesn’t mean the government will send everyone a gun in the mail.

Working, commerce, and social behaviors are all protected in US law to varying degrees.

>“Privileges” aren’t a legal concept. You have the right to bear arms in the US, but that doesn’t mean the government will send everyone a gun in the mail.

"A privilege is a certain entitlement to immunity granted by the state or another authority to a restricted group, either by birth or on a conditional basis. Land-titles and taxi medallions are pronounced examples of transferable privilege. These can be revoked in certain circumstances. In modern democratic states, a privilege is conditional and granted only after birth.

By contrast, a right is an inherent, irrevocable entitlement held by all citizens or all human beings from the moment of birth."

https://en.wikipedia.org/wiki/Privilege_(law)

>Working, commerce, and social behaviors are all protected in US law to varying degrees.

But you said "rights under the constitution."

The constitution guarantees you the right to own and carry a gun. Not to employment, food, clothing, shelter, or the ability to participate in society. The latter are all conditional, dependent upon the market or the will of the state.

The constitution doesn't even guarantee a right to vote (obviously the framers didn't believe such a right should be universal) which is why felons can lose their voting rights. There are amendments like the 15th and 19th amendments which prevent voting discrimination, but an inalienable right to vote doesn't exist in the constitution.

> Not to employment, food, clothing, shelter, or the ability to participate in society.

The Supreme Court doesn’t agree with you.

Rights need not be provided to you for free. You have the right to buy a gun, or an abortion, or a political ad, or a wedding cake - but you’ll have to buy them.