Cecil has been through previous games, therefore she might recognize your character and know a great deal of your character's canon/personality/history/etc.! Of course, it is up to you entirely how she interacts with your character, if she did indeed meet another iteration of them. I can either use an in-game excuse for her to actually forget or have her simply not mention it to your character. Here are some questions you can answer on this!

In addition, Cecil has a spell called "Libra" that usually allows her to "see" the abilities and weaknesses of the target she uses the spell on. Sometimes the spell does not work, however, and Cecil herself will only cast the spell when there is an immediate threat present, but for convenience and just in case you and I do decide to use it for some plot, here is a thing you can fill out for that too! (Please note: this is a general reference sheet for me regarding this ability; I will still always pass it by you first when I consider using it IC if you have given me permission here. If you opt out, I simply won't ever bother you with it!)