I post on LinkedIn, Stack Exchange, and this site using my real name. The benefit of doing so is that I have to keep myself in check and really think before I write - yes, there are edits and deletions - and overall the effect has been very positive for me. Being active on the chemistry SE site has actually proven to be of value in getting jobs related to chemistry - at least 3 employers have said it was useful to se…
This name is pseudo-anonymous. I use it everywhere and am still careful not to 'pop off' too much on it. I also own the username for my real name both here and other places. If someone wanted to track down my real identity, it wouldn't be hard. On Reddit, for instance, I use multiple anonymous usernames alongside my pseudo-anonymous and real name accounts.
How honest and close to my instinctual response depends on my level of anonymity. I think there is some value to saying quick & honest ideas so you can be checked rather than having to worry you will look dumb on your real name and never have those ideas checked. Using anonymous usernames also cuts down on potential stalking or doxxing if someone disagrees.
With that said, I try to be nice and not too inflammatory even on my anonymous accounts. I haven't always succeeded but try to avoid raising my blood pressure over internet arguments that gain nothing.