Re-enter the exchange of registered special rims/special tyres with equal dimensions?

Hello dear community, for my SEAT Leon SC the following tyres are registered as standard: 205/50 R17 93V Currently matured and separately registered is the following: 225/35 R19 93V on LM wheel Tomason 8 5JX19H2 TYPE […] My current Tomason rims are less suitable for the winter and currently only have summer tyres. I fear that the rims could be damaged by the spreading material in winter and therefore wanted to add a more suitable set in the same size. + corresponding winter tyres in the same dimensions (225/35 R19). Now my question: Do I have to register this additionally, even if the dimensions of the tyres and the measurements of the rim remain identical? In my head this would not make any sense, since I could also take every rim suitable for the standard tyres to 205/50 R17 without having to register them. But I am irritated that the rim is registered here extra incl. manufacturer, type name, etc. Dear thanks in advance! Anny