The closest you can get to renaming the lambda function is using an alias, which is a way to name a specific version of a lambda. The actual name of the function though, is set once you create it. If you want to rename it, just create a new function and copy the exact same code into it. It won't cost you any extra to do this (since you are only charged for execution time) so you lose nothing.
For a reference on how to name versions of the lambda function check out the documentation here.