Yes. But, for safety and convenience, your name is not on the share certificate.
The certificate will show that the shares are held "in Drive Wealth's name for the benefit of Hatch customers". This is a common practice in the US called In Street Name.
Note: With Hatch you aren't buying and selling CFDs, you're buying shares.
Why are my shares held In Street Name?
Holding your shares In Street Name doesn't diminish your rights as the owner. Electronic trading is really only possible as a result of holding shares In Street Name. It removes the need to match each share certificate to each customer, which makes settlement faster and reduces the risk of loss and theft that comes with the transfer of physical share certificates.
It also lowers transaction costs, which makes it possible for Hatch to pass those savings onto you.
Who knows how many shares I own?
DriveWealth manages the books and records of the shares, which means they have a record of the number of shares every Hatch customer has in each company and ETF.
You also have access to your monthly account statements and individual order confirmations from the reports section of Hatch. As with any investment, you should always review your confirmations and statements carefully to ensure they accurately reflect your understanding of what cash and shares are in your Hatch account.
Who custodies my shares?
Citi (Citigroup Inc) custodies your shares and is headquartered in New York City.
There are no custodial or management fees associated with your shares.