The rules for a Druid's Wild Shape ability say "When you transform, you assume the beast’s hit points and Hit Dice." But the stat block for "A monster's hit points are presented both as a die expression and as an average number."
Now, for your typical monster that the DM controls, the DM can of course choose whether to just take the average or actually roll for how many hit points it should have. But here, it's a player that's using the monster's stat block.
So, does the player choose whether to take the average or to roll for hit points for their new form? Do they need to roll because the ability to just take the average is a DM-only thing? Do they need to just take the average because that's the standard "monster statistic"? Or does the DM pick each time just like they'd pick for a monster, even though it's for a player?
I'd prefer official sources or references if available. If there aren't any, then I would accept any semi-official or well-informed well-reasoned arguments, preferably backed up by whatever evidence is available. Obviously as with any rules interpretation the DM has the final say, but I'm usually the DM and I'm not sure what to do.
Best Answer
The closest thing I can see applying is that, as a player character, you can choose to take average hit points or roll for them every time you take a level.
I'd make the case that it's always the PC's choice, since it's still the hit points of the PC we're talking about, and with RAW they can choose their HP generation method at any time they roll.
There's no rule that I've found that provides an exception that would allow the DM to dictate PC hit points, or any other character feature choices for that matter. So, unless someone else finds one, I interpret that as being the player's choice.
5E's 'exception based' design principle provides support for that. Crawford has said on record that if a spell or an ability doesn't explicitly define a feature or limitation, then don't infer it to be there. The example was: Fire Bolt says it sets unattended things on fire, so it does. Produce Flame doesn't say that, so you don't have to spend time figuring out if it does or it doesn't; it just doesn't. I would interpret that to mean: since there isn't something specific in the Wild Shape rules, don't infer anything beyond what players already do for their hit points.
Whether they always take average, or always roll, or roll once and keep that number for a given animal for the life of the character... that also seems like a good place for a character-driven decision that becomes part of their flavor, and I'd need something compelling to take that choice away.