I don't have specific knowledge about the changes made in this movie, but I can say that for movies in general, one reason why names are changed on the shooting script is because the Studio's legal department has a veto over all aspects of the production, and can require a name change if there are potential legal problems in using a particular name.
In this case, if EMI's lawyers saw a potential problem over the use of any of the names in the book, the director would be contractually obligated to make the necessary changes.
This was a film made in 1974, from a book published in 1934. Character names that were not seen as a problem in 1934 by the author might easily have become problematical in the intervening 40 years.
And because it was an adaptation of a book, such changes stand out: on a normal picture it would not be at all obvious that a character's name had been changed since the initial draft of the screenplay, which would never be seen by anyone outside of the production.
Minor changes in other character names would be made at the discretion of the director, Sidney Lumet, or at the suggestion of the actor playing the part.
The director can have his own reasons for making changes. In this film, having seen it on tv many times (it's a popular Christmas favourite in the tv schedules in England), it's my personal opinion that the Belgian chef-de-train was made into an Italian because American actor Martin Balsam (1919-96) could not do a convincing Belgian accent -- partly perhaps because Poirot is Belgian too, so that on screen Balsam would be going head-to-head with Albert Finney as Poirot, and any shortcomings in Balsam's Belgian accent would thus be emphasised by the contrast with Finney's. Realising this difficulty, Balsam may have requested this change.
The director's motive for changing the name of the English valet Masterman to Beddoes is pretty obvious, since for American audiences he would have wanted an English valet to have an obviously English name. Masterman is too neutral, and might be from anywhere. To tie down the character as definitely English, in keeping with the performance he wanted from the actor, it makes sense to give the character a more suitable name.
Likewise with the French maidservant Paulette. To an English audience, there is nothing very French about the character's original name, Suzanne. So it needed to be changed, to give the character greater credibility with the audience.
For Caroline Martha Hubbard, perhaps there was some legal difficulty. But maybe the director simply disliked the name, Martha Hubbard, as sounding too much like ''old mother Hubbard''. There is no point giving a character a silly name, if you're not making a comedy. It hampers the character needlessly.
So if I'd been Sidney Lumet, making a big international picture, those are the changes I would have made, in addition to any problems raised by the lawyers. Albert Finney is still around, living quietly in retirement, so you can ask him what Lumet actually said.
Actually, I might have cast Peter Ustinov as Hercule Poirot, rather than Albert, but that's another story (a personal preference, in my opinion, based on the strength of Ustinov's performance in Death on the Nile, not any shortcoming on Finney's part).