Yes I understand there is probably nothing can do with the label text since it's limited by the text bar. What I'm thinking is something like simple color or number labels. Even a number doesn't really show what project it's in, at least it refer to same project before user closed it.
The label is definitely easy to read in Cmd + Tab, though I find it's slow to cycle through the whole list when I can just click the dock icon to switch.
I also tried dock magnification, it helps with label but I need to wait for sometime before selection because the process is not linear and predictable, while with static dock I can move and click immediately.
I found there is a Eclipse plugin for similar problem. You can customize the badge string through that plugin. If we can have something similar in RStudio project settings (either a literal string or some pattern applied to project name, like only take first several letters?), that may help. Though I'm not sure if a shorter label will have larger font. It may not solve the problem (a single number should be recognizable even with same font).