Questions about optimizing execution time should use the tag: performance.
Questions about minimizing memory should use the tag: memory-optimization.
I like the idea of speed-optimization and memory-optimization.
These two have obvious benefits. I think speed-optimization is more clear than performance (to me, memory is part of performance...), and making them more clear what they mean without reading the description I think is important. I don't think many people read the descriptions... (I don't always... and new users certainly don't)
I don't like the idea of code-size-optimization.
For starters, I don't think this is particularly useful. Why does the lines of code matter? Moreover, is refactoring and removing duplicated code ever going to not be mentioned in at least one answer to a question?
And this isn't Code Golf... so we shouldn't really be seeing answers that rewrite code into really silly obfuscated stuff just for the sake of being short.
And how many times would this tag actually even be used?
If the user were asking for something more like reducing the size of the compiled binary file, that might be a different story (perhaps it needs to run on an embedded system with very little storage space?)... anyway, on the whole, I'm not sure this particular tag is very good or useful.
Finally, I believe memory-management is being used where one might otherwise use memory-optimization, and to me, these are two extraordinarily different things.
If I wrote some code that involved manual memory management and I'm particularly interested in having that aspect reviewed to make sure I've done it correctly, then I might want to use memory-management. Importantly, this tag is for use when you're more concerned about making sure you're managing your memory correctly and optimally (memory-management and speed-optimization might make sense together if you're concerned about the rate at which your memory is allocated or deallocated).
Meanwhile, memory-optimization should be used when not when I'm concerned about how I'm allocating or deallocating my memory, but instead when I'm concerned with how much memory I'm allocating and interested in doing everything feasible to minimize my application's memory footprint.