For designations that were selected to a dropdown, you can attempt to track down the Designation Display Name by editing the donation form in NetCommunity and reviewing the Designation Display Name. Note: this assumes no changes were made to the form since the donation was made. 

For Other designations, where the donor typed their desired Fund, this information is not stored in The Raiser's Edge. It's only visible when the transaction is within the NetCommunity plugin, prior to linking it to a fund. Once the fund is linked in the plugin, the free form text disappears and shows the linked Fund.