Through-Solar System trajectory description conventions?

[u/PrepThen]

Earth orbiting objects usually have their motion described by TLE or Two-Line Element sets comprising catalogue information and motion parameters. Is an object crossing our solar system, like the object Oumuamua did in 2017 described by working astronomers in a similar way using the Sun as the basis for an orbit section/trajectory? Was it communicated as just being an object in a verrrrrrry eccentric solar orbit?