As soon as I change the title of a record (i.e. the string in the record list), a search for a word which was only present in the filename (for example a reference number of a downloaded invoice) does not yield any results anymore.
If you need a “display name” for the document while retaining the file name, then use Spotlight Comment for the display name – and include that property in the columns for document lists. Both Spotlight Comment and the name are searchable in DEVONthink. (DEVONthink also supports “Aliases” for a document, but for some unexplained reason “Aliases” are not searchable.)