Yes all bananas do go brown when in the freezer.
The frozen bananas are still good to eat and safe to eat when they turn brown in the freezer but they may taste a bit different.
Frozen bananas are usually good to mix with ice cream or other recipes such as banana bread where you won't notice the taste change.
But you certainly can eat them after thawing the frozen bananas even when they turn brown.
It's best to peel the bananas first and then place the bananas into a freezer safe container or a Ziploc bag and then freeze them.
The frozen bananas will last for up to a year before they start to go bad in the freezer.
You can freeze bananas with the banana peel on but it is harder to peel the banana when the peel is left on.