No, it is not possible to change the mass of an atom's nucleus without changing its atomic number and element name. The atomic number of an atom corresponds to the number of protons in its nucleus, and each element has a unique atomic number. The number of protons determines the element's identity.
The mass of an atom's nucleus is primarily determined by the combined masses of its protons and neutrons. Protons and neutrons have similar masses, so the total number of protons and neutrons in the nucleus largely determines its mass. If you were to change the mass of the nucleus, you would need to add or remove protons or neutrons, which would alter the atomic number and, consequently, change the element.
In summary, the mass and atomic number of an atom are closely linked, and changing one would require changing the other, resulting in a different element.