Your display name will be part of the unique URL for your user profile (ie: writers.work/jennifer).
Because of this, the display name should be all lowercase letters and numbers, with no spaces or special characters.
The display name you want may not be available if it is already being used by another Writers Work member. In that case, try out some different variations of the name. So, for example, if the display name "johndoe" is already taken, you could try out "doejohn" or "johnhdoe" instead.