The vast majority of the time, I take showers in the morning.
However, there is the odd time that I shower at night. When I do this, I put deodorant on afterwards. My reasoning for doing so is basically just in case I forget in the morning. I know it's probably worn off over the night, but still. At least a little bit might be left, right? A little bit is better than none!

Also, sometimes, I have trouble sleeping at night. So if I'm awake until 4am, and have to be up at 7am, I'll just take a shower and try to sleep some more after my 4am shower. I don't imagine it would wear off after 2-3 hours, so yeah, I put it on then.