Teams decide who can start a conversation with whom in Messages. Each person in a team is either a Manager or a Member:

A team's managers can message everyone in the team.
Its members can always message the team's managers.
Members can message each other only when the team has Allow members on this team to message each other switched on.

Someone in several teams can message everyone any of their teams allows. Every approved user is added to the default team automatically, which starts with no managers and members not allowed to message each other — so until you make someone a manager or switch that on, nobody can message anyone through it. Edit Team warns No managers on this team when that is the case. Roles with permission to message anyone in the organisation are not limited by teams at all.

When staff start a new conversation, they only see the colleagues they are allowed to contact.

Step 1
Open Teams
In the side menu, open Admin Settings, then click Teams. Opening Teams needs the teams feature and the team read permission.
Step 2
Read the Settings column
Members Can Message means the team's members can message each other. Managers Only means members can message only the team's managers. The default team is marked Default and sorts first.
Step 3
Open the team
Click the team to open Edit Team. Editing a team needs the team edit permission.
Step 4
Let members message each other
Under Who can message whom, switch on Allow members on this team to message each other. Leave it off to keep members talking to managers only.
Step 5
Managers are always reachable
Whatever this setting, members can always message the team's managers — Edit Team spells this out on the Members row.
Step 6
Choose the managers
Under Members, change a person's role from Member to Manager. A changed row is tinted yellow until you save. Add people with Search and add members..., or remove them with the cross.
Step 7
Managers reach the whole team
A team's managers can message every member of it, whether or not members can message each other.
Step 8
Save
Click Save Changes. The team's row now reads Members Can Message.
Step 9
Creating a team
Click Create Team, enter a name, and choose whether members can message each other — new teams start with it on. You can add initial members there, or later from Edit Team, where you also choose the managers.
Step 10
Messaging anyone
To let a role message anyone in the organisation regardless of teams, give it the messaging Contact anyone permission in Admin Settings → Roles.