No, an atom cannot have an atomic number equal to Graham's number. Graham's number is an extremely large number that was first defined in the field of mathematics. It is much larger than the number of atoms in the observable universe.
The atomic number of an atom corresponds to the number of protons in its nucleus, which also determines its elemental identity. The atomic numbers of known elements range from 1 (hydrogen) to 118 (oganesson). These numbers are relatively small compared to Graham's number, which is estimated to be around 10^100.
Therefore, Graham's number is many orders of magnitude larger than any atomic number observed in nature, making it impossible for an atom to have an atomic number equal to Graham's number.