I recently changed insurance companies.

After receiving the paperwork I noticed they added the car as a KL instead of KJ since the year of the car is 2003.

Would this cause issues?
I prefer the higher market value of the KL personally

It can yes, technically it's fraud. I only found out recently my wagon was under as a TR. Made sense then as to why they wouldn't insure it for more

Would this cause issues?
I prefer the higher market value of the KL personally

You might, but your insurer would beg to differ. You will need to amend the details, as it is your responsibility to confirm the details are correct. If your vehicle is insured as anything other than what it actually is, you open yourself up to being denied claims (potentially making you liable for third party claims) and cancellation of your policy.

Pretty much if they have the VIN number correct and the engine number if they wanted it then they cannot argue really.
Biggest stuff up i saw was two red barina's brand new.
Dealer got the rego plates muddled up as delivered same day. Old lady of one promptly put it thru a butcher shop window.....
Insurance company says hmm your driving the wrong car madam. They had correct Vin though on insurance so payed up once they worked out what happened.
Had new BMW bike a few years back let rego lapse then re- registered 2 years later.
Blue slip etc get to RTA and bike does not exist on database sir.
Get VIN rechecked please.
Did that and its correct. Get old paperwork and find RTA originally entered VIN wrong so from new was not technically registered or insured.
If i had a insurance claim company would straight off when assessing check VIN and engine numbers if they donot match can reject claim.Vee