Health insurance companies and employers will generally recommend a bank that insureds can use to establish an HSA once they’re enrolled in an HDHP, but enrollees are free to select any HSA custodian they like.
If you’re enrolling in an HSA through your employer, you’ll likely need to use the HSA custodian that your employer selects in order to have your pre-tax contributions payroll deducted and in order to receive any contributions that your employer makes on your behalf. But once the funds are in your account, you’re free to transfer them to another HSA custodian if you choose to do so.
A long list of banks, credit unions, and brokerage firms offer accounts for saving and growing HSA funds over time, so shop around before you select an HSA custodian. The saving accounts include a dizzying array of options. And brokerages offer countless stocks, bonds, and funds to invest in with low trading fees, while others may have limited choices, are more expensive, and have hidden fees (HSA Search is a useful tool showing fees charged by hundreds of HSA custodians, but it is by no means an exhaustive list of all the available HSA custodians; check with your bank, credit union, or brokerage firm to see what they offer as far as HSAs, and what fees they charge).