I would write the character name on the back of the item, or better yet what I do is have an archival backer card with the name of the person and what they did, and attach it to the photo with archival photo corners. The former may be perferable since it is a DVD slipcase.

As for value, no one can predict whether or not Ezra Miller will be remembered even 10 or 20 years from now. So I wouldn't worry about it. What I would be concerned about is provenance if you do decide to sell it - keep some sort of item about the red carpet event with the DVD slipcase or next to it. This way someone who may decide to buy it will go, "Ah, he was at the event, and can prove it."

I recently got an autograph from Ezra Miller on my Batman V Superman DVD slipcase and just from a personal stand point when it comes to major sci fi and superhero films I like to get the character the actor or actress plays written under there signature. This is for two reasons first, because I think it just looks nice and 2nd as a memory trick because some signatures are basically chicken scratch and there is no way to make the name out so by having the character name written there as well I'll always know even when I'm old and senile that so and so was played by him/her. Now unfortunately because it was a Red carpet event where I met Ezra he didn't have time to do this.

What I'm curious about is if I write the character name under the signature would it decrease the value of the item? I don't intend to sell this item but again you never know so I don't want to write it in under his signature and make the item worthless unless it would have no effect on the value because his signature would still be there unaltered. So I just want to get a conceneus from the community on this before I do anything thanks.