a library where I can put in all non-UI related code that I want to share between iOS apps (networking, filesystem, logic, algorithms, data structures)
Don't you think it's a really bad idea?
The purpose of (1) naming things and (2) having libraries is to make it easier to find things. By putting unrelated stuff in the same library, you go against this purpose. What's the point in having a library in the first place, and in finding a good name for it? If your colleague asks you: “Where do we have the ETL code?” and your answer is: “Look in the
HugeLibraryForEverything library”, does the name actually matter?
If you really want to have one and
BigMess isn't an option (although it's quite representative),
Common would seem explicit enough, since the purpose is to share code among applications. However, I would strongly recommend to have at least some sort of code organization, and to have specific libraries for specific purposes. That networking stuff can go to
YourCompany.IO will contain the file system stuff. As for the logic, algorithms and data structures, they would find themselves where they belong to, accordingly to what they actually do, instead of being put together just because they are data structures or algorithms. Think about it, why would a stream compression algorithm be in the same library as the sorting algorithm?
Once you have a clear structure, finding proper names for the libraries should be a bit less difficult. I won't assert that it's easy, but at least, you wouldn't be in a situation where you search for a name of a bunch of things which have the only common point of not being something else.