I will walk through this problem:
1. I make a new assy, Solidworks calls it "Assem1" in the title bar.
2. I make or add some parts and then do some designing 'in context' of the assembly. E.g. make virtual parts, or add externally-saved parts and make references between them.
3. I hit Save or Save As and change the name Assem1.sldasm to something more descriptive like Giant-killer-robot.sldasm, and click Save, but then I get an error dialog that says parts are going out of context because I'm creating a 'new' assembly file, and you should rename all the parts etc. It seems that Assem1.sldasm was already saved somewhere automatically.
This seems to be a new behavior as of SW2015. In previous versions of SW I was able to start a new assy, make parts, and then hit Save and give it any name I want and it was done.