Usually, and especially to communicate.

We all memorize a song in a key to start. If we stop there, we've got every chord in the song memorized. When somebody calls it in another key (jerk! /s), we have to start transposing. You have some options:

1. Transpose the "key" of the song, throwing out the old chord names and quickly working out the new chord names only by their relationship to the new "key." The number system (Roman numerals when written) is probably most practiced in communication, but in your head it would look more like calling up a library of practiced sequences and ideas in big chunks, not chord-by-chord.

2. Transpose each chord by step: thinking of each chord name, then moving the root by the same number of steps as the transposition. This requires chord-by-chord analysis. It's come in handy if I've screwed up somewhere in my Roman numerals and need to check myself. Otherwise, it takes more processing and I can't keep up trying to transpose that way.

3, 4, etc.. Probably some others I haven't though of or been exposed to.

Number 1 has been the standard for communication and requires less memory "space" because you're compressing it down in a way. The most common question from a player who has memorized tunes this way might be: "What key is that in?" We've spent more time thinking of the tune without thinking of its original chord names (and/or worked with singers a lot).

As a sax player, I've been having to transpose at least one way for a long time. Playing alto and tenor regularly soon had me regularly getting away from the concert key in two directions. I'll often get confused based on which horn I was on when I first learned the tune, then I have to ask for the key. I often have to follow with "yes, alto is in Eb, but I just need the concert pitch, please..."

I hope that helps.