What is the correct name for this sea?

The geography is the same. The answer depends on where you stand.

BM-101 Northeast Asia basemap showing Japan, the Korean Peninsula, eastern China, and the Russian Far East

Japan

Sea of Japan
Official government usage.

South Korea

East Sea
Official government usage.

North Korea

Korean East Sea
Official government usage.

International usage

Sea of Japan
Predominant label on international maps.

The geography is fixed. The label carries perspective. The same sea can appear under different names depending on who is making the map.

What else on a map might look objective but carry a point of view?

Context: the naming dispute is unresolved. Hanten is not choosing a preferred name here; the exhibit shows how map labels can carry history, politics, language, and perspective along with geography.