When you create an EndNote Library (ENL), the default is to call it 'My EndNote Library'. You can keep this name or rename it. The important thing is to only have one EndNote Library. When your insert your references into your Word document, the EndNote toolbar in Word 'talks' to your EndNote Library. You need to make sure that it is only talking to one ENL. If you need to organise your references, do this within your ENL using groups (see How to organise your EndNote Library).
You should always save your active EndNote Library to your local directory and NOT to cloud storage e.g. your OneDrive. See:
There have been instances of EndNote Library corruption/loss of data when EndNote libraries are saved to OneDrive/cloud storage.
If you need to use your EndNote Library on more than one device or share your references/library with colleagues/friends, then you can do this by syncing with EndNote Web, see:
We recommend EndNote desktop is your 'main' library and the online version is used for syncing, for sharing references/libraries, to use on a tablet or as a backup library.