That's exactly how it should behave. Removing the $ before the column label
makes the defined name range column-relative, row-absolute. This means it
will reference the cell in the same row, but whichever column the active cell
is located in. If you want to constantly reference an absolute cell, give it
another name than the one used in the formulas.

Maybe the following will help. It assumes that you want to determine
identical calculations for Income, Expense, and NetIncome across several
columns. This is a typical scenario for say comparing a P&L or Balance Sheet
for multiple periods, each located in their own columns. Here's the layout:

In the Define Names dialog:
Define income cells:
NameBox entry: SheetName!Income (makes it sheet level)
RefersTo: entry =SheetName!B$2:B$8
(makes it absolutely rows 2 to 8 across all columns)

Define total income cell:
NameBox entry: SheetName!TotalIncome
RefersTo entry: =SheetName!B$9
(makes it absolutely row 9 across all columns)

Define expense cells:
NameBox entry: SheetName!Expenses
RefersTo entry: =SheetName!B$10:B$20
(makes it absolutely rows 10 to 20 across all columns)

Define total expense cell:
NameBox entry: SheetName!TotalExpense
RefersTo entry: SheetName!B$21
(makes it absolutely row 21 across all columns)

Define net income cell:
NameBox entry: SheetName!NetIncome
RefersTo entry: =SheetName!B$22
(makes it absolutely row 22 across all columns)

Adjust the rows for income and expense ranges to suit.

Now you can set up your sheet for mutiple lists, each for separate periods.
Not all income or expense cells need to have values. Put descriptions in
column A for each income/expense category, and the totals. Here's what it
will look like:

1 Period1 Period2
2 Income1 0.00 0.00
3 Income2 10.00 15.00
4 Income3 10.00 20.00
....
9 Total Income 20.00 35.00 (Formula is: "=SUM(Income)"
10 Expense1 2.00 0.00
11 Expense2 7.00 10.00
....
21 Total Expense 9.00 10.00 (Formula is: "=SUM(Expenses)"
22 Net Income 11.00 25.00 (Formula is:
"=TotalIncome-TotalExpenses")

If you need more help then post back to email a sample file.

HTH
Garry