Is there a known standard data structure which is a hash table that resolves collisions using a binary tree? If so what is the name of this data structure? I imagine such a structure would be useful as it should reduce the worst case search time down to O(log(n)) compared to O(n) in a hash table, and the best case would still be O(1).
Yes, but there isn't a standard name for it shorter than what you've already written.
[...] by using a self-balancing tree, the theoretical worst-case time of common hash table operations (insertion, deletion, lookup) can be brought down to O(log n) rather than O(n). However, this approach is only worth the trouble and extra memory cost if long delays must be avoided at all costs (e.g. in a real-time application), or if one must guard against many entries hashed to the same slot [...]
and that's pretty much the reason why.
Knuth came up with the name "ordered hash table" for this bucket collision strategy, which can use any of the many log n search data structures. Most people are not aware of that and in practice I've seen only KyotoDB using it. Most others switched from simple linked lists to open addressing schemes (double hashing, Cuckoo, Robin Hood) for better cache performance.
"Ordered hash tables", O Amble, D Knuth 1973 http://comjnl.oxfordjournals.org/content/17/2/135.full.pdf
You can use a balanced tree, a trie, or just a simple ordered array with binary search, since mostly the bucket size will be < 8. It mostly a cache issue, so you will not want to use many pointers for a tree.