Here's the display name shown by opening the same postgres connection using ODBC vs connection_open():

Or a similar but SQLite connection:

tmp <- tempfile()
dir.create(tmp)
dbplyr::nycflights13_sqlite(path = tmp)
con <- connections::connection_open(RSQLite::SQLite(), file.path(tmp, "nycflights13.sqlite"))
con <- DBI::dbConnect(odbc::odbc(), driver = "SQLite", database = file.path(tmp, "nycflights13.sqlite"))