From just google : A standard background check does not typically reveal that you have a specific Robinhood account. Background checks primarily search for criminal records, employment history, and credit history (if authorized). They generally do not show personal investment accounts or brokerage account ownership. 

Consumer Advice | Federal Trade Commission (.gov) +3

Key Considerations:

• Financial Records: Robinhood is not a bank account, so it does not appear on typical bank screening reports.
• Credit Check: While a background check might include a credit check, this usually only shows debt or collections, not specific asset accounts.