The first thing I would recommend is to become familiar with the differences between the Assembly version and the File version. Unfortunately, .NET tends to treat these as the same when it comes to the AssemblyInfo files in that it usually only puts AssemblyVersion and allows the FileVersion to default to the same value.
Since you said this is a shared assembly, I'm assuming you mean it's shared at a binary level (not by including the project in the various solutions). If that's the case you want to be very deliberate about changing the Assembly version as that is what .NET uses to strong name the assembly (to allow you to put it in the GAC) and also makes up the "assembly full name". When the assembly version changes, it can have breaking changes for the applications that use it without adding assembly redirect entries in the app.config file.
As for naming, I think it depends on what your company naming rules are (if any) and the purpose of the library. For exmaple, if this library provides "core" (or system level) functionality that isn't specific to any particular product or line of business, you could name it as:
CompanyName.Framework.Core
if it's part of a larger library, or simply
CompanyName.Shared
CompanyName.Core
CompanyName.Framework
As far as when to increment version numbers, it's still rather subjective and depends on what you consider each portion of the build number to represent. The default Microsoft scheme is Major.Minor.Build.Revision, but that doesn't mean you can't come up with your own definitions. The most important thing is to be consistent in your strategy and make sure that the definitions and rules make sense across all of your products.
In almost every version scheme I've seen the first two portions are Major.Minor. The major version number usually increments when there are large changes and/or breaking changes, while the minor version number usually increments to indicate that something changed which did was not a breaking change. The other two numbers are considerably more subjective and can be the "build" (which is often times a serial date value or a sequentially updating number that changes each day) and the "revision" or patch number. I've also seen them reversed (giving Major.Minor.Revision.Build) where build is a sequentially incrementing number from an automated build system.
Keep in mind that the assembly major and minor versions are used as the type library version number when the assembly is exported.
Finally, take a look at some of these resources for more information:
http://msdn.microsoft.com/en-us/library/51ket42z.aspx
http://msdn.microsoft.com/en-us/library/system.reflection.assemblyversionattribute.aspx
http://blogs.msdn.com/suzcook/archive/2003/05/29/57148.aspx