The important thing for the BE core is that the assembly name is BlogEngine.Core. A name like BlogEngine.Web is just a folder name ... so it shouldn't matter what you call it.
If you make changes to files outside your theme, then a repercussion is you need to make those changes again when upgrading. Whenever possible, if you can limit changes to your theme files, it makes it much easier to upgrade.
You might not remember all the changes you made to BE 1.5. The best thing to do is to use a file comparison tool, like Beyond Compare, to compare the modified 1.5 code you have now to the original BE 1.5 code. This will identify what you changed.
You can then upgrade to 1.6 and reapply those same changes you made to your new 1.6 blog.
There were some SQL schema changes. There's an upgrade script in the setup\SQLServer folder.
For upgrading, I usually just overwrite all my files except for the web.config file, robots.txt file and the App_Data folder. Of course, first have a backup in case something goes wrong.
There's a lot of changes in and outside the BE core between version 1.5 and 1.6. So no, you cannot just replace the BE core DLL.
upgrade instructions from BE 1.5 to 1.6.