As the title suggests, can the Adventurer search be updated to include Trial Characters linked to Family?

I had bought a name change coupon prior to the deletion of non-transferred game data and used the following resource to check if the character name, Travesty, I wanted was available.

https://www.naeu.playblackdesert.com/en-US/Adventure?region=NA&searchType=1&searchKeyword=Travesty 

Even now when I check the name shows as no result, but its clearly taken. Could the Adventurer search be updated or the naming policy on trial characters be changed?

Thanks.

Wrong section, but yes the website should also include trial character, at least the names of em.