Create a list using Capital IQ:

• Go to Screening > Companies
• Under Company Details, click Company Type and select Private Company.
• Under Company Details, add any desired criteria relating to industry, geography, etc.
• Under Company Details > Company Statistics, you can add Year Founded (relatively recent) and Total Amount Raised (mm) to identify young companies who have received significant amounts of funding.

Create a list using Preqin:

• Go to Search for > Companies & Deals
• Select Company Search from the left-hand menu
• Using the filters at the top of the page, you can screen for companies using Year Founded and/or Total Amount Raised. Under More filters > Historical financials you can also add % Revenue Growth YoY to your screening criteria.

Use published lists:

• American City Business Journals Book of Lists: Many local business journals for specific cities in the U.S. publish books of lists that include fast growing companies. Note: Some cities' lists  (ex. Chicago, Los Angeles) are available only in print in the Stamps Reading Room (ask at the desk for help). 
• Forbes Lists (ex: World's Most Innovative Companies, Small Giants: Best Small Companies)
• Fortune Rankings (ex: 100 Fastest Growing Companies)
• Inc. 5000
• FormDs.com  Nearly all startups and investment firms file Form Ds with the SEC when they raise money.  Form D filings contain: amount of money raised, equity or debt insurance, insurance category, names of the executives and directors, addresses for the company and brokers used and commission paid.