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Is there an index

There is no such index of algorithms implemented in Sage.

or an easy way to search for this? An example of this is the Berlekamp-Zassenhaus algorithm for factorising polynomials over integers.

You could use the search functions search_def, search_doc, or search_src to search through the Sage source tree. When someone implements an algorithm or interfaces to an algorithm from a Sage package, the name of the algorithm should be mentioned in the docstring of the relevant module, class, method, or function. For the Berlekamp-Zassenhaus algorithm, I got this

sage: search_src("Berlekamp-Zassenhau")
rings/polynomial/polynomial_element.pyx:2656:        ## NTL uses the Berlekamp-Zassenhaus method with van Hoeij's improvements.

That should tell you where to start looking, specifically in the file sage/rings/polynomial/polynomial_element.pyx around line 2656.