Do any elements have the same atomic number?
No, because each element has its own specific property, BUT certain elements have similar properties, like elements in the same family.
The atomic number is associated to the element's composition for one atom, in which the atomic number = number of protons in the atom with a neutral charge.
If you look at the Periodic Table, each element has its own atomic number, usually increasing by 1 from left -> right ; top -> bottom. Meaning each element has more protons in their atoms than the previous. This continues all the way to 118 (for now - until scientists discover more elements).
Hope this helps :)