Since you didn’t tag with a country code, you are likely to get US centric answers.

Mine is that when I opened a business checking acct, I was given a stamp. business name, acct number, for deposit only. I stamp and deposit via phone app, which snaps pictures of both sides. No signature.

I don't see any benefit to putting the least amount of text you can on a stamp. It normally says

For Deposit Only to

ABC Bank

Account 1234

XYZ Company

The bank name helps if the check were to be misdirected in processing and the account name for verification if your account number is miskeyed somewhere. This helps prevent headaches and lost checks. Ask your bank for the final word.

However, there is one important recent change due to potential fraud. If you are using mobile or remote check deposit, you should now endorse it

For Mobile Deposit Only To

or

For Remote Deposit Only To

or your check may be rejected by your bank.

Is that enough? Do I have to sign in addition to this? Do I have to include the business name also in the endorsement?

Ask your bank. You need to ask them what is the information they want you to include on the stamp to properly endorse the check. You also need to ask them if it changes if you are scanning the checks and sending them the images.

Once you know what they require, you also need to make sure that whatever stamp you order, it fits within the space designated on the back.

The Federal Reserve Board implemented new rules in July 2018 that are changing the requirements banks are imposing for deposits through mobile apps. These are mostly to try to mitigate the risk of you trying a scheme to deposit the same check in multiple banks before they figure out what you did.

"...under the new rules, if the member wrote “for mobile deposit only” or similar on the back of the check deposited via RDC, Financial Institution A would not be liable if the member later managed to deposit the paper version of the check at Financial Institution B."

Source: "CUs Begin Using New Rules 'for Mobile Deposit Only'" - Credit Union Times