The stuff that counts will remain intact.

The more players fill out their completionist checklist in each region, the more Renown rewards they earn.

And, these prizes carry over.

Diablo 4 unique items

From the map screen, open Region Progress (W on PC).

It also seems that some players are reporting that their Renown is not carrying over to the second season.

However, those rewards may not show as being unlocked on the Renown screen.