while cancelling process of Ur partnership firm registration there u will find the option :Reason for cancel, select the option : Change in Constitution of business, leading to change in PAN , but further it will Ask u to Provide the GSTIN of the transferee entity(prop. firm) under the Details for Change in Constitution section. System will validate the same, and based upon itโs Legal Name of Business, will auto-populate the Trade Name
that's why I ask u apply new registration for proprietary firm first then cancel the no. of Ur partnership firm