Most shuls make a mishebeirach for those who take on the fast, it’s in the siddur.
Usually people who take on private fasts (behab is not communal), do not advertise
to the world that they are fasting.
Many places have minyanim for Mincha, that layn parshas vayechal and haftorah of dirshu,
which can be done when there is at least six or seven of the minyan fasting.