Not exactly the right forum, but I took delivery of a Ludicrous P100D Model X on June 28. I also got the Dual Motor badge with underline.
I was able to order the Model X badge and the P100D badge from my local service center.
I tried asking both Tesla Support via email, and my local service center in person whether it's possible to change the screens to say P100D instead of "Performance Ludicrous Mode" but email support gave me a stock reply about what changes can be made to the car's avatar (like color and wheels), and the tech at my service center said that my car's config can't be changed from what I paid for (despite my attempt to explain that P100D and Performance Ludicrous Mode are the same config, just displayed differently).
Also, there are a couple interesting anomalies in the API data for my car. There's no trim_badging key in my vehicle_config. Consequently (I believe), in the Tesla app, I see no text beneath where it says "Model X" at the bottom. I would expect to see P100D or DUAL MOTOR (with underline). Can anyone with a dual motor-badged S/X confirm if your app also shows like this?
Also, my option codes are completely screwed up. I have a Model X (MDLX) with deep blue metallic paint (PPSB) and [hopefully] Autopilot Hardware 3 (APH4).
AD15,MDL3,PBSB,RENA,BT37,ID3W,RF3G,S3PB,DRLH,DV2W,W39B,APF0,COUS,BC3B,CH07,PC30,FC3P,FG31,GLFR,HL31,HM31,IL31,LTPB,MR31,FM3B,RS3H,SA3P,STCP,SC04,SU3C,T3CA,TW00,TM00,UT3P,WR00,AU3P,APH3,AF00,ZCST,MI00,CDM0
So my Model X is actually a Model 3 (MDL3) with solid black paint (PBSB) and AP2.5 (APH3) in disguise.