Customize fields shown on Linked Field Record Selector

Is it possible to control the fields that are shown for each record in the selector (see: https://support.airtable.com/hc/en-us/articles/206452848-Linking-to-Another-Record#link-unlink)
for example to reorder the fields or change which ones appear?

the image: https://support.airtable.com/hc/article_attachments/360024978113/blobid2.png.