If the name changes, but the general details of your work did not change, then there's nothing wrong with using the new name. It is an accurate description of what you are currently doing, and of what you have been doing this whole time. In general, position names in the workplace (and on resumes) are descriptive, rather than formally defined. As long as the title you put on your resume accurately describes the work you did, it doesn't necessarily have to be something you were officially called at any point along the way.
Now, there are some caveats to that. The first is that some specific position titles do have clear and important meanings, and you don't want to claim them if they don't apply. Do not claim a role as a Professional Engineer if you did not have or were not using the applicable license. That's not a problem in this case. More in general, position titles often indicate or imply things, and it's not a good thing to pretend to those titles if those things that aren't true (again not an issue in this case). For example, don't call yourself Team Lead if you were not, in fact, leading a team. Finally, if you're working for a particularly large corporation, their titles often will have formalized meanings, and it's possible that the recruiters will know what those are and what they mean. In those cases, it might be best to stick with the official name. This, too, appears to not be an issue in this case.
Outside of those caveats, though, if the title you use is a good description of the position you had (and in this case it seems to be so) then it's fine... and if you got the new title without any change in responsibilities, there's every reason to think that it's a good description of the position you have.
