Title basically. If it needs clarification, imagine the US picked up and moved to Canada, and was still called the US, even though it owned none of the original lands.
Are you asking about the ruling class/government or wholesale movement of people as well?
In theory, your question can be satisfied by any of the modern, Germanic, Slav and Turkic states, formed by the descendants of ancient people who underwent migration from their original lands, and conquered another population. These migrations were well-documented such as that of the Bulgarians or the Magyars.
Savoy. The Duke of Savoy became the King of Piedmont, but the family remained the House of Savoy. In 1859 following the war with Austria-Hungary, Piedmont gained Lombardy and the Italian Duchies, but gave Savoy to France. Hence the Duke of Savoy, whilst King of Piedmont and ultimately King of Italy, no longer included Savoy in his domains.
Hungary. It was first located in what would now be Ukraine, and it slightly moved to the west. In 1400 it was basically above current Greece.
The Roman Empire. Circa 1100 it had lost its remaining holdings in the Italian Peninsula and with them the original homeland of the empire was forever lost.
Another example may be the Turks, who would eventually conquer the Roman empire and now reside in its former (final) heartland. But I do not know the history of Turkic peoples that well so as a follow up I ask if this statement is true?
Armenia is also a case in point. The Armenian Kingdom of Cilicia does not overlap with the Armenia of today or the Armenian Empire of antiquity.