The association of Suzuya with the number "13" is a word play: its possible to write the name "Juuzou" with the kanji translating to "thirteen". 13 (XIII) is also the Death Arcana. Apart from the grim reaper parallels it can represent loss, conclusion, sadness, transition into a new new state, psychological transformation and deep change. The number can also be associated with his hair clip, his quinque, his association with Jason and working on the thirteenth ward in the Oneshot Joker. It's also considered an unlucky number in many cultures and is associated with death, betrayal and loss.
During Anteiku raid, one of Suzuya's hair clips went missing, reducing his number down to 12 (XII): referencing The Hanged Man, or "Change", hinting that he would change in some way.