Add the table name to a column using VSTACK.

Hogstad_Raadgivning Inspired by the earlier answers, the attached file contains a dynamic solution that does not require hard-coding of the table names in the EXPAND or VSTACK functions.

Though you need to add two formulas on the sheets that contain the tables you want to stack. In my example I added in A4 a formula like:

=tablename[@Måned]

Hide column A if you don't want to see this formula!

Then in B1 of every sheet I pick-up the table name with:

=MID(FORMULATEXT(A4),2,FIND("[",FORMULATEXT(A4))-2)

Hide row 1 if you don't want to see the table name!

The stacking formula then looks like this:

=VSTACK(EXPAND(t_appelsin,,4,Appelsiner!B1),EXPAND(t_plommer,,4,Plommer!B1),EXPAND(t_pærer,,4,Pærer!B1))

Change the sheet names and/or table names, and all will be updated dynamically. Though you need to press F9 to see the changes.

Hogstad_Raadgivning 

 How about this?

http://e.anyoupin.cn/EData/?p=tools.consolidate.consolidateshts/consolidateSheetsSkipRows

Hogstad_Raadgivning 

You can create a simple LAMBDA to add the table name to any column, thought it does use INDIRECT, so may have performance impacts on workbooks with many calculations or large datasets:

ADDTABLENAMECOLUMN = LAMBDA(tableName,
    LET(
        tbl, INDIRECT(tableName), 
        EXPAND(tbl, , COLUMNS(tbl) + 1, tableName)
    )
);

This works because we can pass the string version of the table name to INDIRECT to return a reference to the Table. 

We can then use it in your formula, like this:

=VSTACK(
    ADDTABLENAMECOLUMN("t_appelsin"), 
    ADDTABLENAMECOLUMN("t_plommer"), 
    ADDTABLENAMECOLUMN("t_pærer")
)