The Roman Map of Britain Ixio or Iaccio ? River Itchen, Hampshire
Axium (R&C 237) next
Axium could be the result of /Ixium, the remaining six (or five) minim strokes after x are anyone's guess.
The Itchen is first recorded as Icene, (on) Icenan 701.
CDEPN has Celtic *iak- *ik-, W. iach 'healthy' as a potential root. If so, then Axium might represent an original Iaccio where I was taken to be a text divider, and o misread as û (= um).