There was a discussion a few years ago regarding this topic here:
viewtopic.php?t=17768
Since then the handbook has been updated but seems to say pretty much the same thing but in a new place:
General Handbook 29.5
The general feeling there was that it may be appropriate to pay essential funeral expenses from fast offerings in some cases but less essential expenses are more appropriate from budget. But there isn't a hard and fast policy in the handbook which means the bishop and stake president have the keys to determine the most appropriate course.
As for listing the recipient, that isn't stated anywhere that I know of. I would probably recommend the surviving spouse or family if in the ward since it would be their ability to pay that would determine whether fast offerings should be used. But if the deceased does not have family in the ward then listing the deceased may be necessary.