The challenge of integrating hydroxyapatite nanoparticles (nHAp) with polymers is hindered by the conflict between the hydrophilic and hygroscopic properties of nHAp and the hydrophobic properties of polymers. This conflict particularly affects the materials when calcium phosphates, including nHAp, are used as a filler in composites in thermal processing applications such as 3D printing with fused filament fabrication (FFF). To overcome this, we propose a one-step surface modification of nHAp with calcium stearate monolayer. Moreover, to build the scaffold with suitable mechanical strength, we tested the addition of nHAp with diverse morphology-spherical, plate- and rod-like nanoparticles. Our analysis showed that the composite of polycaprolactone (PCL) reinforced with nHAp with rod and plate morphologies modified with calcium stearate monolayer exhibited a significant increase in compressive strength. However, composites with spherical nHAp added to PCL showed a significant reduction in compressive modulus and compressive strength, but both parameters were within the applicability range of hard tissue scaffolds. None of the tested composite scaffolds showed cytotoxicity in L929 murine fibroblasts or MG-63 human osteoblast-like cells, supporting the proliferation of the latter. Additionally, PCL/nHAp scaffolds reinforced with spherical nHAp caused osteoactivation of bone marrow human mesenchymal stem cells, as indicated by alkaline phosphatase activity and COL1, RUNX2, and BGLAP expression. These results suggest that the calcium stearate monolayer on the surface of the nHAp particles allows the production of polymer/nHAp composites suitable for hard tissue engineering and personalized implant production in 3D printing using the FFF technique.