Susan Mordy
In the Developer Version you have more control of things like that. if you go to the attribute config file for your app:
arcgis-web-appbuilder-1.0\server\apps\##\configs\AttributeTable\config_Attribute Table.json
then you can change the name there.
For the AGOL version I agree with zhongren Gu you need to change the name of the layer in the mxd and then republish.