I have received a check made out to
My Business Name
My Personal Name
My Home address
Formatted like that.
Can I deposit it in my personal checking account?
The important thing is who is owed the money.
Say your company owns a car worth $10,000 and you sell it. The seller has given you a check for $10,000. The money must go to the company, increasing its profits and its corporate tax bill, else the IRS or HMRC or whatever your tax office is called will come after you for tax evasion.
It's no problem to pay the money into your private account and immediately transfer it to the company. Or to pay the money into your private account and record it as a loan given by the company to you. In both cases, the company will have more profit and pay more taxes.
If your company is a partnership with multiple owners, and you put money owed to the company into your own private account without telling anyone, that is probably theft or embezzlement.
Obviously if that car was your own private car, then the money should go into your own private account. If it went into the company account and was then transferred, the company would have to document very clearly what happened in case there is an audit.
It is fine to deposit it either way, the bank won't care.
Typically, if you use online or ATM deposit, the bank doesn't even look if there is any match - unless someone asks them to, because he misses a check.
Note that whichever way you deposit or cash it has no impact on your tax situation - it still counts for whatever it counts, if it has any tax relevance.