In the NT there are five people named "Alexander":
- A son of Simon, Mark 15:21
- A member of the High-Priestly family during NT times, Acts 4:6
- A Jew is Ephesus involved in the riot, Acts 19:33, 34
- An apostatized Christian, 1 Tim 1:19, 20
- A coppersmith who did Paul "great harm", 2 Tim 4;14, 15.
Are these all separate people or are some the same? We do not know. It is possible that Alexander #3, #4, #5 could possibly be the same person; or just Alexander #3 = #5; or any other combination.
We do not have enough information to say. However, the fact that Alexander #3 and Alexander #5 are both copepersmiths suggests they are the same person.
Ellicott suggests that Alexander #3, #4,  are all (possibly) the same person but he is not certain.
Barnes thinks that #3 & #5 are the same person but cannot be certain. Other commentators are similarly vague and non-committal.