ConnectedMeshComponents

ConnectedMeshComponents[mr] gives a list {c1, c2, ...} of disjoint path connected meshed regions.

Examples

Find connected components of a mesh:

mesh = BoundaryMesh[Ball[{0, 0, 0}, 1]];
ConnectedMeshComponents[mesh]

Multiple disconnected regions:

r = RegionUnion[Ball[{0, 0, 0}], Ball[{5, 0, 0}]];
ConnectedMeshComponents[BoundaryDiscretizeRegion[r]]

Please visit the official Wolfram Language Reference for more details.