If you live close by your county clerk or other government office that handles assumed name filings you can walk in, give them your signed & notarized certificate, pay the fee and the clerk will take your certificate and either:
Physically stamp it and give you a copy
Scan & digitally stamp it then give you a copy
This is your proof that the certificate and your business name has been filed. Your bank will need to see the stamped certificate when they open your business bank account.
If you do not live close by your county clerk or other government office that handles assumed name filings you will mail your signed & notarized certificate, to the correct office with attention to "Assumed Names" or whichever name your state uses. different states use different names such as: Trade names, fictitious names, business names, etc. The appropriate name will be on the top of your certificate.
It is a good idea to call your county or state office to get the room number for the address. You may or may not need to send it certified mail ;this is a good question to ask the clerk when you call.
Once the certificate and business name is filed you will most likely be sent a physical copy of your stamped certificate. It is possible they will email you a copy as well to save time. You can ask the clerk to email you a copy in your letter. Your bank will need to see the stamped certificate when they open your business bank account. It is up to the bank if they will accept a copy or need to see an original certificate.