For example I have a menu block with menu elements:
.menu
.menu__element
.menu__element--current
But lets say .menu block is contained inside another block, .header
How to deal with naming in this case?
.header
.header__menu
.header__element
or
.header
.header__menu
.header__menu__element
or
.header
.menu
.menu__element
The menu should be a class unto itself so .menu should suffice. If it's a menu that is ONLY in a header and never anywhere else, then .header-menu. Then you can point to the menu directly without going through the header class.
If you prefer to do it the way you outlined, then .header_menu.