The Record ID is alreday shown on Customer Details, but isn't searchable. So what you really need is to add a custom field for a Badge ID. Adding a field and putting it on the Custoemr Details dialog is covered here:
http://campgroundmaster.com/news/add...othecusto.html
Any custom fields are automatically searchable using Find Customer, so that's covered.
However it sounds like your real question is how to get the record ID into that field automatically, so you don't have to enter it each time. For this I would recommend adding an Event Action, with the trigger "New reservation, after". Thre isnt' a trigger for new customer, but it's probably safe to assume that they don't really need a badge until they're actually renting a space anyway, so this should work fine.
The action to set the field would use the function SetFieldText(rRecord, cFieldName, cValue), e.g.:
SetFieldText(ThisCust(), "Cust_User_Badge_ID", FieldText(ThisCust(), "Field_Index"))
This would probably also put the "#" in the field, so if you don't want that then you can use the Mid() function to trim if off, eg:
SetFieldText(ThisCust(), "Cust_User_Badge_ID", Mid(FieldText(ThisCust(), "Field_Index"), 2))