Hi gb,
As SG has noted, the first error is the added = sign. The first = typed opens the formula editor, which displays ƒx to indicate this is a formula. The editor box will not display this =.
Here are three images of the formula editor. The first shows your start at constructing the formula using the mouse (or trackpad), the second your (unfinished) edit of my formula, copied and pasted to your table, and the third my 'unswitched' formula from cell A2 of the two column table in my post showing only two tables.

One advantage to building the formula references using the mouse is that it automatically includes as much of the cell or range address as needed. Here the blue lozenge shows a reference to the range of cells A2 to C100 on the table named "Table 1" on the sheet named "OSIA #2870 Roster-1".

In the copy/paste/edit version Upper of these two images), the first instance of the table name "Main" has been replaced with the sheet name "OSIA #2870 Roster-1", and no table name has been entered.
For a cell reference:
to a cell or range on the same table as the formula, Numbers needs only the address* of the cell.
to a cell on a different table from the formula, but on the same sheet, the name of the Table must be included.
to a cell on a table on a different sheet from the formula, the name of the Sheet must also be included.
(If no other table in the document has the same name as the one containing the cell, the Sheet name
may be omitted.
(range reference requirements are similar)
*"address" can be the full column&row address, of may include only the column letter. If only the column letter is used, Numbers will interpret it to mean "all cells in column X", "all cells not in Header or Footer rows in column X", or "the cell on 'this row' of column X", where 'this row' is the row containing the formula.
Both "Main" references should be changed to the same table.
"tablename::A2:C100" in your has several consequences:
- Row 2 of the Table is row 1 of the indexed area, so a row index generated by ROW() in cell A2 of the table containing the formula will return data from row 2 on the indexed area (which in row 3 of the Table containing the data. The list supplied to the email manager will start with Aiello, not with Adams.
- Even if the C100 reference is made absolute ($C$100), this reference will adjust when rows are removed from the table or when rows are added to the table between row 2 and (currently) row 100, the row may not adjust to include rows added to the end of the table.
- While the email list table requires data from only the first three columns (A,B and C) of the main table, setting these three into the formula means the range will have to be edited whenever the formula is used for a different table requiring data from later columns.
Changing the range reference to an absolute columns only reference covering all columns of the table eliminates these concerns:
- Row 2 of the table (where the data starts) is row 2 of the indexed area, and data will be returned to the same row of the table containing the formula as it is in on the data table (Main).
- Specified using only the Column references, the indexed area always includes all the rows of the data table.
- Setting the range to include columns A to the last column of the table, and omitting the number parts of the beginning and end addresses allows the same formula to work on any table pulling data from the Main table with no changes to the formula.
Suggestion:
You should see the formula you copied from here, displayed in format showing that Numbers has accepted it as a formula.
If so, click the green checkmark to confirm it, and check the see that it has provided the expected result.
If so, you can rename your data table (currently "Main") to the name of your choice. Numbers will automatically revise the formula to match the new name.
Fill the formula into the rest of the rows and columns on the Names and email table.
Regards,
Barry