Okay, based on Daniel Hom's response here http://community.tableau.com/thread/117100
I tried to "Rename" in the Measure menu and that did the trick.
But I am still curious to know why I wasn't able to right click and "edit alias". This has worked for me earlier. In the same worksheet, I have another table in which I have done this and it works fine there!
Can you attach the packaged workbook? so someone can explain you the issue.
One possibility I can assume is, number of records converted to discrete (Right click - > Convert to Discrete) and placed in the row/column. In this situation you cannot change the alias.
If it is continuous and treated as a measure then you can change alias.
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Number of Records is simply a Tableau generated field that contains the number 1. Just create your own field with your own field name (My Number of Records) and put the number 1 in it. Use yours instead of Tableau's and you shouldn't have any problem.