> Debugger puts me into a context where I have to figure out what `p` stands for.

`p` stands for "the process in question".

I like to think of single-character vars as idea or topic headers that track the single thing I'm currently up to. I'm rarely working with more than one at a time, frequently it's the only variable, and there are contexts where I wouldn't use them at all.

IMHO if you're in a situation where `p` isn't obvious to you, "something has gone wrong".