Yes, if you will be filing as Married Filing Separately you have to use two separate tax returns, one for you and one for your spouse. Each tax return can have its own address.
However, you should be filing as Married Filing Jointly. From a tax standpoint it is the best way to file when married. You can file jointly even if you do not actually live together. The address on the joint return can be where you receive your mail, so either address can be used.
See this TurboTax support FAQ for filing jointly versus separately - https://ttlc.intuit.com/turbotax-support/en-us/help-article/taxation/better-married-couple-file-join...
