CB has no functionality to dynamically alter the title of a Joomla menu item to append something like that. I'm not aware of a Joomla event to even do that from a plugin as if there was one it'd likely be possible using CB Auto Actions. If such event exists it's likely one of the generic content events. See Joomla documentation below regarding its events.

docs.joomla.org/Plugin/Events

Regardless we've no plans to directly implement something like that. Private message count can be output in your CB Login Module, CB Workflows Module, above profile on the CB Menu, and outside of profile by substituting in the CB Menu tab. It'll also be possible in the future to easily substitute just the icon shown on the CB Menu tab.

I am sad that cb cant't have this functionality.

Nothing can. I'm not aware of a Joomla event for menu items to modify their titles before display. If it exists then it'd be an interesting usecase for CB Auto Actions.

Canyou tell how to make Private message count output above profile on the CB Menu, and outside of profile by substituting in the CB Menu tab ?

It should already be displayed on their profile as an envelope icon. To display CB Menu outside of profile see our substitutions tutorials below.

www.joomlapolis.com/documentation/279-community-builder/tutorials/18353-using-substitutions-throughout-cb
www.joomlapolis.com/documentation/279-community-builder/tutorials/18354-substituting-tabs-as-fields

Maybe you know how to make in cb new messages count colour as in picture above?

The envelope icon has a CSS class around it you can use to change the color as needed. Right click and inspect element on the envelope to use your browsers developer tools to see available CSS classes.

There's a CSS class specifically surrounding the envelope. Use your browsers developer tools to review that class by right clicking on it and clicking inspect element. This will open your browsers developer tools where you can review the HTML structure carefully for CSS classes.