I tend to think that if you are a doctor, a lawyer, a teacher, or someone else in a position people consider one of authority, it is a good idea to keep your online discussion largely anonymous, except for where you are actively seeking to establish or improve your professional reputation. Given how much social interaction happens online, it makes it really hard to do utterly normal things, like vent about work or commiserate with others in your field about shared frustrations, under your real name when almost everything is public and searchable. I can't, for example, vent about my students online under my real name (and I proceed with extreme caution even under a pseudonym), or I risk my job. Using a pseudonym makes sense for a lot of reasons, and maintaining an online presence under my real name also makes sense for a lot of reasons, but in different contexts.