Rotating the data frame in ArcMap using the tools from the Data Frame Tools toolbar does not rotate the labels in the data frame.
This is a known limitation.
1. Close any ArcMap and ArcCatalog sessions.
2. Open the ArcMap Advanced Settings utility file from the ArcGIS for Desktop installation folder.
This file is usually located in the following location:
C:\Program Files (x86)\ArcGIS\Desktop10.3\Utilities
1. In ArcMap, activate the Labeling toolbar by navigating to Customize > Toolbars > Labeling.
2. Activate the Maplex Label Engine by clicking the Labeling drop-down arrow > Use Maplex Label Engine.
3. Click the Labeling drop-down arrow > Options.
4. Open the General tab, and check the 'Rotate point and polygon labels when data frame is rotated' check box in the Data Frame Rotation section, and click OK.