Amina Inloes is originally from the US and has a PhD in Islamic Studies from the University of Exeter on Shi'a hadith. She is the program leader for the MA Islamic Studies program at the Islamic College in London and also the Managing Editor of the Journal of Shi'a Islamic Studies.
A person is allowed to change their name even if there is nothing inherently wrong with their birth name.
Whether there is a relationship between one's birth name and one's soul is a more difficult question. I am not aware of anything in our religious sources that discusses this apart from that on the Day of Judgment it is said that people will be addressed by their names and their mothers' names (apart from Shi'i texts which say that the Prophet's descendants will be addressed by their names and fathers' names), but it is hard to say without being there whether that will be a recognizably verbal utterance of a name or just some means of identifying us that we will understand. Also, there are situations where the Imams (A) informed people of their birth names (as part of demonstrating their comprehensive knowledge) and perhaps there is a hint of some significance there. But in those cases it seems that the birth names were changed due to circumstances and not because the person actually wanted to be identified by a different name.
So, I think the best answer to the first question is that maybe there is a relationship, but if there is, it isn't something that is focused on in the Twelver Shi'i tradition.
Certainly the Prophet (S) did not see a problem in encouraging people to change their names where necessary.
As a side note, although I've never seen this discussed, I would imagine that some of the mothers of the Imams (A) were not born with the names they were born with because their names are usually given as Arabic/Persianate whereas some of them were said to come from far-off regions, so perhaps some of them acquired these names during their life journey.