If you right click in your control chart's FrameBox, then select Customize, you will see a Text item for each phase. Internally these are known as TextSeg display boxes.
If you lookup TextSeg in the Help>Scripting Index>Display Box>TextSeg, you will see the available messages. From the FrameBox customize UI you can change font, color, size, style, transparency. With JSL you can also change the text.
Currently, there is no method to change the position (that I know of) in the active chart report. You can create a dead "picture" of the chart with changed the positions, using journal boxes. However, it takes a bit of coding.
If your phase names are running together, I suggest you create a simple column called Phase ID (values like 1, 2, 3 or A, B, C) and use that for the phase variable. Then append to your control chart title (the Phase Limits table or elsewhere) the key of Phase ID to Phase Name. A trivial example using Big Class is shown below. The script is attached.