Obi Dome is a decorative accessory put on a Obi JIme cord.
Typically it is put on so-called Sanbu Himo which is a short and little thin Obi Jime though larger Obi Dome can be put on regular Obi Jime.
In general, you don’t use Obi Dome for formal kimono, but this is not because Obi Dome is for casual use but because formal kimono use thick Obi Jime therefore it is merely difficult to put it on. So, it’s common to see people attend to ceremony wearing Homongi with Obi Dome.
However, It’s better not to use Obi Dome for Tea ceremony. It doesn’t suit for Tea ceremony which values simplicity and also there is a norm not to bring in hard materials with you to the ceremony for it might cause some damages on tea items.
There is no strict rule for Obi Dome, so as long as it goes good with kimono, you can pick whatever you like. Some people arrange their brooch to make it.
There is a type of Obi Dome you put it on after you tie Obi Jime not before you tie it. This type is easier to use but you have to be careful because sometimes it falls.