Before the Roman conquest todays Lombardy was called Gallia Cisalpina ("Gaul on this side of the Alps").

During the Republic, Gaulia Cisalpina was subdivided into Gallia Cispadana and Gallia Transpadana ("Gaul on the other side of the Po river"). Lombardy was part of the latter.

Augustus reorganized administration of Italy into regions and Lombardy was part of the 11th Region, Transpadana.

Diocletian divided the Empire into dioceses and Milan was the capital of Italia Annonaria and a part of diocese Aemilia and Liguria.

Constantine was also a great reformer who divided the Empire into Prefectures and Lombardy was part of the Prefecture of Italy Africa and Illyricum, Diocese of Italia Annonaria, province of Liguria and Aemilia.

Under Theodosius, province of Aemilia and Liguria was divided into separate administrative divisions and Lombardy was part of the latter.

During the Reconquest of Justinian, todays Lombardy was again part of province of Liguria.

This naming might seem strange, but consider that Lombardy was a name given centuries later and what is now known as Liguria was calledd Alpes Cottiae. Also all these provinces, regions and dioceses overlapped with and included areas which are different from what are today regions of Italy.

Citations:

W. Eck, L’Italia nell’impero romano. Stato e amministrazione in epoca imperiale

Pierfrancesco Porena, La riorganizzazione amministrativa dell’Italia. Costantino, Roma, il Senato e gli equilibri dell’Italia romana

The scope of Lombardy has changed extensively in time. Starting with the Lombard invasion of Italy, "Langobardia" described the whole territory held by the Lombards, as opposed to "Romania" which was still held by Romans (Byzantines). Langobardia was divided in two by the territory between Rome and Ravenna, and the two parts became known as Langobardia Maior (north) and Minor (south, basically the dukedoms of Spoleto and Benevento).

Langobardia minor eventually went out of use, especially after the Lombard dukes and gastaldi were taken over by the Normans in the 11th century. On the contrary, Langobardia maior (now simply Langobardia) continued to define the Kingdom of Italy, whose capital was Pavia and whose crown was the Iron Crown of the Lombards. Even after the fall of the Lombard kingdom, Carolingian and Ottonian kings were crowned as Kings of the Lombards. Lombard identity was in fact so strong that when the Italian City-states (Comuni) revolted against the Holy Roman Emperors in the 12th century, they named their alliance "Lombard League". It included towns all across the Po plain, from nowadays Piedmont to Veneto and even Genova and Bologna. By that time Tuscany had already was slipping out of the Lombard identity, so much that Dante and Petrarca make a clear division between the two. With the rise of Venice in the East, Lombard identity was supplanted by Venetian one, and the whole idea of Lombardy waned as the region was divided in dukedoms and princedoms. The dukes of Milan had a special interest in keeping Lombard identity alive, as they held Pavia and Monza (where the Lombard crown is kept). They never pushed a claim to revive the Kingdom, but their expansionists ambitions were clear, in fact so clear that all other Italian powers, and especially the Papacy, did everything they could to cancel Lombard identity in other lands and weaken the potential claims of the Visconti/Sforza dynasty. With the fall of the duchy of Milan, Lombardy came to designate the territories around Milan, held in turn by the French, the Spanish and the Austrians. When Napoleon conquered northern Italy, he created a Cisalpine Republic, not a Lombard one; but after his fall Metternich created a kingdom of Lombardy-Venetia, mostly to avoid claims to other parts of Cisapline Gaul which were not under Austria's power. The kingdom was conquered by Piedmont in 1859 and became part of the kingdom of Italy. The name of Lombardy was once again revived after WWII when Italian regions were created in 1947 and one of them was named Lombardy. It included the same territory as the old kingdom, which was split on the Mincio; additionally, Lombardy was extended to Lomellina and Oltrepo Pavese, not originally under Austrian rule.

Administrative borders still seem to fail cultural divides, since for example the area of Novara and Ossola (Piedmont) and that of Italian Switzerland still speak a language classified as Lombard, which is the same spoken in all areas of Lombardy.