Assuming by db_name you really mean the table name, maybe you want 
something like this:

def db_query(tablename, fieldname):
    query = (db[tablename].Financial_Institution == auth.user.id) & (db[
tablename].Completed == 1)
    return db(query).select(db[tablename][fieldname]).first()[fieldname]

Do you really have multiple tables with Finacial_Institution and Completed 
fields, and do you really need to do the same query on these tables, except 
for returning different field values? Otherwise, it's not clear how useful 
this function is?

Note, if you have a DAL table or field name in a variable, you can use 
db[tablename][fieldname] and row[fieldname] syntax rather than 
db.tablename.fieldname and row.fieldname (the latter syntax using dot 
separators represents attribute retrieval and requires the literal 
attribute names, not variables holding the names).

Anthony

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