FBI on function with concatenated string
Are the columns nullable ? is the query a LIKE ? Is there an NLS issue ?

I'd expect a 

upper("LAST_NAME"||','||"FIRST_NAME"||"MIDDLE_NAME"||"SUFFIX_NAME") = :bind


to use a index range scan

upper("LAST_NAME"||','||"FIRST_NAME"||"MIDDLE_NAME"||"SUFFIX_NAME") LIKE :bind


may use a index fast full scan or a table scan depending on whether columns from the table were likely to be required. If it thinks 1 in 5 rows will match and that for each of those it needs a column not in the index, then it would be slower to use the index+table lookup than a straight table scan.

It could be the table is very small and it isn't worth using the index.