If the InterRail officials tell you that it is better to change the pass, it is better to change the pass.
Passports are often checked against the name on the pass in some countries and less often (to almost never) in others, and in several countries the train people will see Alex and Alexander as the same name, in other countries they may make a case out of it just because they can.
Likely oneOne fine and losing the pass (as it does not belong to this person, see the name is different) is likely more expensive than the name change.