"Mediolanum" is latinized, but Celtic in etymology (in Gaulish, it would be "Mediolanon", meaning "middle plain" or "middle plaza". Cognates for Gaulish "lanon" exist in Old Irish ("Lann" - meaning "thin", "plate" or "layer") and Welsh ("Llan" - meaning "parish" or "yard"). If the word was Latin, it would be "Medioplanum".
Also, yes, one Mediolanum was modern-day Milano. But, such places existed across the Celtic-speaking world:
- Mediolanum of the Santones in Gaul (modern-day Saintes)
- Mediolanum of the Aulerci Eburovices (modern-day Evreux)
In addition, Ptolemy lists two places named "Mediolanum" in Germania:
- one was located probably along the Morava river, near the place it mounts in the Danube.
- the other one was located at the left-bank of the Rhine, in an area that roughly corresponds with the modern-day northwestern Ruhr Area (I've seen people claimed that the town Borken is at the site of Mediolanum, but in my opinion, that is a guess).
In a similar fashion, towns named "Brigantium" also existed across the Celtic world, including Bregenz, Austria, and Briançon, France.