Almost all Aeoniums die after they flower, but only the actual rosette that flowers. The rest of the rosettes which do not flower will live on. If your plant branches (which I'm pretty sure it will do, given time and space) then you can enjoy the flowers without losing the entire plant. Typically that is years down the road in any case.
Your plant looks to be in excellent shape at the start of summer. Be aware that these plants follow a seasonal cycle of winter growth and summer rest. So if the rosette shrinks up in coming weeks, it's probably just doing its natural thing, nothing to be overly concerned about. Just good to be aware of. Certainly not a sign that you need to provide extra water.
An expert could tell you the exact ID of your plant, but Aeonuims are not simple to identify. I grow about 30 different kinds and only have firm names for a handful. Presumably you would need to see a flower to have the best idea. Fortunately the name doesn't matter much in terms of care. At some point in the near future (maybe fall) you might consider a bigger pot if the plant has filled up the one it's in now.