Badge, license plate and radio are all the same number. Historically, their weapons also bear their number. When weapons are replaced, you get to purchase your issued pistol.
Unless things have changed:
The troopers select their number in the final phase of trooper school. If you had a relative with GSP, (father, uncle, etc.) you may get preference to get their old number. Should a certain number become available later, you can request it. Even the Governor and First Lady had a radio number at one time (GSP 1000 and 2000, I believe).
As a side note, Corporals and Sergeants receive a framable warrant upon promotion. Lieutenants and above receive a commission. Troopers even salute the officers...
Lieutenants and above drive completely unmarked cars with uniforms being optional. At one time, cars issued to the top brass were loaded with factory options, unlike the regular troopers. One Colonel had two state cars, one marked and one unmarked. This particular Colonel also had a free personal car supplied by Ford Motor Company...