If I applied for credit under my business name and used my EIN number instead of my social security number, can the company put that against my personal credit?
I cannot answer your question accurately because you did not include enough information in your message. You did not mention how your business is organized. If your business is a properly organized and operated corporation then you have limited liability for the debts the corporation incurs. If your business is a sole proprietorship or partnership then you have liability for the debts the business incurs regardless of what information you provided the lender when applied for the loan.
You use the phrase "can the company put that against my personal credit" which leads me to believe you are asking if the payment history on the business loan or credit card will be reflected on your personal credit history. Again, this depends on how your business is organized. If your business is a corporation then the corporation has its own credit history that is separate from the employees, owners, and directors. After all, IBM's or GM's creditworthiness is not reflected in the credit scores of those companys' employees, to pick two examples.
To learn more about how credit scores are determined, see FICO Score Calculation.
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