While I do agree that it is time for a rebrand of the party name, I believe choosing Libertarian Left would be a mistake.
Most of us here are educated around the political process, naming conventions, left / right split, etc. However I suspect the vast majority of voters are not. Libertarian is too close to Liberal (especially when shortened to Lib), and like it or not, is tainted by American politics. Left, while descriptive, may not make sense to many voters.
We need something that is both descriptive and easy to understand, I just don’t think that LibLeft is it.