I resent the remark that it is a "Malaysian thing".
The real truth of the matter is that the rules here are the same rules that are in force in many countries of the world.
There a 3 separate things that is relevant here.
1. Ownership - This is the registration card. The legal owner of the car is the one shown on the registration card.
2. Roadtax - A car must have a road tax disc in order for it to be used on the road. It is renewed yearly or shorter. it can be done anywhere i.e. Post Office, Online etc. The requirement during renewal is that there must be Insurance Cover (in the name of the legal owner) and the presentation of the registration card.
3. Insurance Cover - A car must have insurance coverage when being used on the road.
The answer to your question is that there is NO relationship between the roadtax renewal and legal ownership of the car. Renewing the road tax does not change the legal ownership of the car.
Although you can still renew your road tax, the legal owner of the car is not you. You can continue to use the car with the understanding that you use it with permission of the legal owner. If you are indeed the owner of the car I do suggest that you have the ownership changed. This will require the signature of the current legal owner on the form for Tukar Hakmilik at the JpJ, to avoid such complications.
The insurance Cover shall also always be in the name of the legal owner i.e. The name that appears on the registration card. You an drive the car either as a named driver or the cover is for all driver.
During road tax renewal, you need to buy insurance cover in the name of the legal owner. If you are renewing thru traditional means, then you presnt teh registration card and the counter will check this againt the cover note which is online. If you are renewing is online, then no registration card is required. So you can continue renewing your roadtax without a registration card.
In any case, you should not have any problems in the insurance claim because if the payment is made by the Insurance company direct to the workshop or in the name of the insured. You have go make a deal with the insured.