Use awk:
awk -F'.' '{ print $NF }' infile
The $ in awk is an operator that returns the content of the corresponding valid field.
fields in awk are splitting based on the FS (Field Seperator), which default is Tab(s)/Space(s) (Note: with default FS, all the leading/trailing whitespaces will be ignored too and if you wanted to capture them and so capture thr empty first/last fields then you will need to specify the FS as a regex type.). the FS can be changed with -F switch or via awk internal FS variable.
The NF in awk represent the last field, so by $NF we are telling to print last field's content based on the dot . as the FS.