I wonder if this thing in turn has something in orbit around it? At the size I wouldn't surprise me if it had satellites of its own in orbit, leaving open the question of what to call them. (I'm no astrophysicist, is this really possible I don't know, but it wouldn't surprise me. What would surprise me is if we could detect them)
https://en.wikipedia.org/wiki/Subsatellite:
“A subsatellite, also known as a submoon, moonlet or informally a moonmoon, is a "moon of a moon" or a hypothetical natural satellite that orbits the moon of a planet”
It might be helpful to describe gravitational relationships with human generational terms of parent-child, grandparent-grandchild, sibling, cousin, etc. So the Sun is the Moon's gravitational grandparent and Jupyter is its parent-sibling (Aunt/Uncle, maybe pibling upwards and nibling downwards).
I had to look it up and it is theoretically possible, they could be called sub moons or moonmoon. I'm partial to the name moonmoon personally.