As you have renamed the worksheets, you need to use the new names in the
formula. Also, as you have spaces in the names, you need to put the
worksheet name range inside single quotes. So the formula you need is:
=SUM('Pat Pettett:Sue Fisher'!C10)
Now, if you insert a new sheet BETWEEN 'Pat Pettett' and 'Sue Fisher' it
will be included in the SUM. However, if you insert the new sheet before
'Pat Pettett' or after 'Sue Fisher', it will not be inside the range and
will therefore not be included in the SUM. Also, you must not delete or move
either of these worksheets, or things will go wrong.
What's often done in such circumstances is to have two blank sheets, called
maybe 'Start' and 'Finish', which you never change, and you use the formula
=SUM(Start:Finish!C10)
Your 14 sheets would be between these two sheets. Adding/deleting/moving
worksheets in between 'Start' and 'Finish' then works properly.