That may not have been the best analogy...
Assuming I have this data set:
Sheet3
<table style="font-family:Calibri,Arial; font-size:11pt; background-color:#ffffff; padding-left:2pt; padding-right:2pt; " border="1" cellpadding="0" cellspacing="0"> <colgroup><col style="font-weight:bold; width:30px; "><col style="width:50px;"><col style="width:33px;"><col style="width:37px;"></colgroup><tbody><tr style="background-color:#cacaca; text-align:center; font-weight:bold; font-size:8pt; "><td> </td><td>A</td><td>B</td><td>C</td></tr><tr style="height:18px ;"><td style="font-size:8pt; background-color:#cacaca; text-align:center; ">1</td><td style="text-align:left; ">Person</td><td style="text-align:center; ">Cats</td><td style="text-align:center; ">Dogs</td></tr><tr style="height:18px ;"><td style="font-size:8pt; background-color:#cacaca; text-align:center; ">2</td><td style="text-align:left; ">John</td><td style="text-align:center; ">5</td><td style="text-align:center; ">6</td></tr><tr style="height:18px ;"><td style="font-size:8pt; background-color:#cacaca; text-align:center; ">3</td><td style="text-align:left; ">Sally</td><td style="text-align:center; ">3</td><td style="text-align:center; ">6</td></tr><tr style="height:18px ;"><td style="font-size:8pt; background-color:#cacaca; text-align:center; ">4</td><td style="text-align:left; ">John</td><td style="text-align:center; ">5</td><td style="text-align:center; ">6</td></tr></tbody></table>
If I set a pivot table and make a calculated field called "Total", I'll give it the following formula:
=Cats +Dogs
If I delete the Cats column and refresh my pivot, I get the #NAME? error. When I look in my calculated field, the calculated field is then:
='#NAME?' +Dogs
That's what I believe happened when you deleted that column and, the analogy I was trying to make was that the error you're experiencing is like a #REF error, in that it won't automatically be corrected when you readd the column. you'll have to manually edit the calculated field in your pivot table to get rid of that #NAME? error, just as you'd have to manually edit a cell with the #REF error.