Yes. You can upload multiple files to any specific record whose name is known. 

First, you need to select the object from the "Select Object" drop-down.

After selecting the object, you need to select "Search Mode" as "Search" and enter the name of your required record or any keyword associated with the name of your record.

All the records associated with that keyword from the selected object will be displayed. You can select your required record and upload files to it.