Not resurrecting an old thread (on postnomials in everyday use).
Let’s say I’m a Registered Parliamentarian. Normally I wouldn’t sign things “Saint Cad, RP” but on a resume why wouldn’t I list it. As a teacher, the principal may want a parliamentarian on campus for meeting. But even assuming they don’t, it does show a certain level of scholarship or recognition beyond what another candidate would have. So at what point (or does it?) does it turn into overkill?
When I’m reading resumés, I just find a string of postnominal letters offputting. It’s a bit too “try hard”. It think it’s better to have a separate section headed “Other qualifications”. Or perhaps it could be mentioned in the “Other Interests” section.
And what’s a Registered Parliamentarian?
I think a Registered Parliamentarian is someone with training/expertise/certification in rules of parliamentary procedure, used in formal meetings and such.
I think it’s also relevant to consider that most people would look at the name “Ellerton P. Smithbody, R.P.” and think: what the heck is an R.P.? Having another section labeled “Other Qualifications” would at least enable you to write the titles out in full.
Originally, I thought your title said “polynomials”
If the postnomial is something so impressive that anyone would consider it as much a part of your identity as your name, put it in. Pretty much the only one that comes to mind that meets this requirement is “KBE”.
“Registered parliamentarian” doesn’t even begin to cut it.
“Kool Beyond Existence”? 
Don’t tell me, this a British thing right?
Yes and yes, pretty much: Knight of the British Empire
I thought that was denoted with a prefix instead of a postnomial, though. ie:
“Sir Paul McCartney” as opposed to “Paul McCartney, KBE”
EDIT: Wiki says Paul McCartney is an “MBE”, not “KBE”. Apparently there are a bunch of different levels of knighthood, with KBE being the top. I stand by my “Sir” question, though.
Knight Commander of the Order of the British Empire, the second level of seniority in the order.
And is thus not entitled to the title of Sir.
But if a knight were signing something formally, they would put the postnominals in: a KBE is rather less prestigious than a KG! (Knight of the Garter).
I tried to call someone to have them come in for an interview. Thought to myself “Oh, good. I’ll get a computer technician who’s also a Registered Parliamentarian!”
Imagine my surprise when I realized I’d misread the initials. I wasn’t calling “Arnie Ranklybum, RP”. I was trying to contact “Arnie Ranklybum, RIP”.
This question depends entirely on the position being applied for.
If you work in a professional field that has credentials and specialties, it is expected that they’ll be spelled out after your name. An initial resume sort might happen specifically based on the advanced credentials or applicability of the specializations.
For example, my wife does realtime closed captioning for the hearing impaired on television. Her resume–well, she usually uses a CV rather than a resume–includes CBC (Certified Broadcast Captioner) after her name. It shows that she took the time and effort to join the national association, get their base-level certification, study for and pass a tough certification test, and keep up the continuing education requirements.
If you’re applying for a job working on Cisco networks, and you have a CCIE (Cisco Certified Internetwork Expert) credential, you’d be crazy not to put the initials after your name on the resume to say, “I’m qualified for this job.” It costs over a thousand dollars and takes several days of testing to earn those four letters, and it shows employers you take your skills seriously.