git mv MergeSort.java Mergesort.java
does affect only local version, even you push it to bitbucket, after some other pull repo it does not compile
you on your local env see your changes, but if you clone again, you will get MergeSort.java

step you reproduce:

touch MergeSort.java
git commit -a MergeSort.java -m "add class"
git push
git mv MergeSort.java Mergesort.java
git commit -m "amend file name"
git push
cd .. rm -rf repository-folder
git clone repository-url
ls