There's no universal right to request the name of an airline employee. That would be a matter of airline policy. Many wear nametags, and if you did need to make a complaint (or send in a compliment!), you could identify someone by position and description.
On board, most airlines designate a member of the cabin crew to be the "purser" or "cabin service manager" or some other term that means that they are in charge. Short of the captain, they are the appropriate authority for anything involving the cabin and service on board. If you have a problem that can't be resolved, you could ask to speak to them when they're available. If you later seek to contact the airline, you can say you spoke to the purser, supply your flight information, and they will know exactly who that is.
There is no universal rule that prohibits the photography of airline employees, but it is often forbidden. This prohibition is sometimes explicit: United, for instance, states that "photography or recording of other customers or airline personnel without their express prior consent is strictly prohibited." Other airlines may not have a public policy to this effect, but you may be told it is prohibited if you try, under the catch-all that you need to obey crew instructions. Short of the very much unlikely event of a compelling need to document physical violence (and even then, you could face retaliation), I would strongly advise against attempting to photograph any airline employees without permission.