We point out some properties of \(\eta \) -Ricci–Bourguignon, \(\eta \) -Yamabe, hyperbolic Ricci, hyperbolic Yamabe, and Riemann soliton hypersurfaces isometrically immersed in a Riemannian manifold possessing a concurrent vector field. In particular, we discuss the minimal, the totally umbilical and the totally geodesic cases, as well as the case when the ambient space is a manifold of constant sectional curvature.