withr is often used to temporarily create environments for the purposes of testing. In the tidyverse/r-lib, we try to use certain prefixes to help "jog" function names for people when autocomplete comes up (e.g. stringr's str_*() functions). When you create these environments, you're doing something with the environment in a certain state, hence the use of functions with names following a with_*()pattern (see withr docs for examples).
I don't know who designed the hex sticker, but I'd say the process is roughly functionality → package name → something evocative of package name if there's a sticker. I also don't know why stringr has a violin as opposed to, say, a double bass (or some other use of string). The same holds for the old dplyr sticker, which had slip-joint pliers (the new one has what I think are slip-joint, nose-clamp, and needle-nose pliers, but there's no particular reason flat-nose, linesman, etc. pliers are excluded).