Merit badge counselors are council positions so should show up in the Merit Badge List search visible to unit leaders on the unit’s page.
A unit leader can also see adults in their unit that are merit badge counselors by going to their Roster and selecting Print Roster.
Merit Badge Counselor can see their position by logging into Scoutbook, click on My Dashboard => My Positions.
If there are still issues, check to make sure the member ID in Scoutbook is the same as they have in their registration as a MBC.
If needed, a Council Registrar can push a MBC to Scoutbook by going into their MBC record in ScoutNET and expiring the MBC; wait a day, then add them back.