Accounts with two names are called joint accounts. If yours is one of the two names on a checking account, probably you can close it. You’ll have to check on some things to make sure. Depending on how your account was set up when you opened it, you might be able to close it at will or you may have to get the other person on the account to close it with you.
TL;DR (Too Long; Didn't Read)
If a bank account requires the signature of all account holders in order to close it and withdraw funds, you will not be able to shut it down without the participation of your fellow account owners.
Most joint checking accounts are set up so that the shareholders are joint tenants with rights of survivorship, often known as JTWROS. If one account owner dies, everything in the account belongs to the survivor. While the shareholders are still alive, either account holder can make transactions without the approval or signature of the other. This means anyone on the account can close it, taking all the money. In the event of one owner’s death, the survivor can present a death certificate to the bank to keep the account open but remove the deceased owner’s name. Married couples usually open accounts as joint tenants.
"And" Versus "Or"
You might have opened your JTWROS account as a joint signature or dual signature account. Joint signature accounts require the signature of all the account’s owners to make a withdrawal. Check the statement. If the names on the account are linked by the word "and" (as opposed to the word "or"), then the account requires all the shareholders’ signatures to close it.
Tenants in Common
Owners of tenants-in-common accounts hold shares in the account, usually an equal share, unless there is an agreement stating otherwise. There is no right of survivorship. Instead, if two people equally share the account and one shareholder dies, that owner’s half goes to whomever the shareholder named in his will. To make withdrawals or close this kind of account, all owners’ signatures are needed. Business partners often open accounts as tenants in common.
Tenants in Entirety
In this type of joint account, all shareholders must be involved in any account transactions, signing to approve the dealings. This type of account isn’t available in every state, but several states including Florida, Delaware and Hawaii allow for it; and where it is available, only married couples can open this kind of account. This account has the right of survivorship, so if one spouse dies, the other gets the funds. To remove the deceased spouse’s name from the account, the survivor presents the death certificate.