Can I be liable for using a fake identity to ask about the business model of our competition?

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It depends on the country but in most developed countries you are committing an illegal act by using a fake name to gain competitive advantage.

In the U.S. this will likely fall under under theft by deception and/or fraud. In the U.K. this would fall under "blagging".

In addition of this being an illegal behavior, it is also unethical what you are doing.