SOLVED. Here is a solution that will work - guaranteed 100% - because the information came from the good people at the TDS Central Processing Cell. The entire resolution was by email. You can reach them at contactus@tdscpc.gov.in. No calls, by the way.

When it comes to PAN last name mismatches, each problem is unique. But the following approach will fix it.

1. Examine your PAN card. The fifth character of your ten character alphanumeric PAN number is vital because it represents the first character of your last name.
   
   My PAN is: ****R*****. So, my last name in the PAN database should start with an R. In my case, there are three possibilities: Rajkamal, Rao, or Rukmangada (my official middle name). Spoiler alert: My last name turned out to be not any of these three as you will see shortly!
   
   If your real name is Anil Kumar Jain and the fifth character is a J, then, most likely your last name is Jain. If the fifth character is a K, the last name could be Kumar, Kumar Jain, Kumar Jain Anil, or some weird combination. So how do we know what the last name is?
2. You need another Income Tax document to be sure. The only sure method is to verify details from Form -16/16A/27D (generated through the TRACES website) issued to you by your employer/deductor. It turns out that the “Name and address of the Employee/Deductee” fields are directly drawn from the PAN Master/Database.
   
   The name structure in Form 16/16A/27D is in the following order- First Name, Middle Name and Surname/Last Name. For most people, the information on this form should work.
   
   But even this may not fully solve the issue as you can see from my case below.
3. My Form 16A, which I requested from my deductor, showed my name as Rajkamal Rao. My PAN card shows R as the fifth character. I was attempting to register on the TRACES NRI website. Luckily, this website lets you try multiple times without limit, so all you need is patience to try out different permutations and computations.
1. I keyed in “Rao” into the Traces NRI website. It failed. “Rajkamal” failed too.
2. Frustrated, I sent an email back to TDC CPC. They suggested that I key in the full name, Rajkamal Rao, in the last name field. I did and it worked! Evidently, Form 16 A does not have my first and middle names at all. Also concatenations of your names could work.
4. Conclusion: Rely only on Form 16/16A/27D because this alone contains your PAN name information exactly as it is recorded in the PAN Master. All other documents that show your name (PAN Card, Form 26AS) are not reliable sources.
1. The name structure in Form 16/16A/27D is: First Name, Middle Name and Surname/Last Name. But the names could be combined and concatenated as it happened in my case.
2. If you still run into issues (see my example in bullet point 3 above), contact the TDC CPC at contactus@tdscpc.gov.in. You will not be disappointed with the quality of their response.