I understand the dilemma, but it is confusing.
Ranchi Rajdhani has the issue of both being in the same class having similar number but here,
There's a clear difference here in form of Train Number Series 12xxx 13xxx, class of train (Superfast) etc.
Other Weekly is having stoppage at Lucknow, Rai Bareilly and Varanasi.
It...
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is via Lucknow as written.
This one can simply be Agra Cantt Kolkata Weekly Express. Other one has already been differentiated.
When "via Prayagraj" is not officially used and neither is Prayagraj a halt then why mention it at all to confuse people ?
If it's stopping at DDU after CNB then that's all that matters. Normal people don't care whether it runs via Prayagraj or Varanasi or Jhansi or Banda.
I don't think there's a need to mention Prayagraj in the name here, unless of course it's officially used.
Seniors and Admins should take a call on this.

Exactly.
Even in case of Ranchi Rajdhani also.
Other 2 Rajdhani Trains have already been differentiated in form of via Bokaro Steel City and Via Chopan.
No need to mention Via Japla there when it's not stopping there.
I've...
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had queries from 3 people in last 2 months regarding this same naming system after I had recommended IRI to them.
Some people assumed Agra Kolkata Weekly via Prayagraj was stopping at Prayagraj and halt wasn't updated. I've had to correct them all.
Names shouldn't be confusing here.
Only we care about intermediate stations. Let the names be as they are officially. I seriously don't see a reason to mention non stopping intermediate station in main name of train when the others have been clearly differentiated.