I would invest in a good thumbdrive rather than the travelling library feature. When collaborating on one manuscript with colleagues, it can be a useful feature, however, for your own writing, you want one library which is stable.
If there are two versions of the library now, with some differences, import one library into the other, but be sure that you don’t import duplicates (choose the “discard duplicates” or “import into duplicates library”).
ON A COPY, unformat the paper and reformat it with the combined library. A few references might come up, as they now have a different record number. Select the match (this might give you a clue, if there are some duplicates remaining, so you should go back and delete them.)
If it still happens, inspect those references (edit citation) to see if they are pointing to different records in the libary, but are really duplicates. If so, delete one of the records and unformat and reformat again.
The other time you might get full name/initial, is if they are two different references, but endnote also thinks they are different authors, and want the reader to know that. If they are the same author, replace the first author, by copy and pasting the name from the other record. Often there are subtle differences (an extra space or punctuation) which Endnote reads a differences.
Finally, whenever you use the Unformat command, you turn off CWYW. If you want the word document to automatically format citations and references when you add or delete them, you need to turn it on again thru the format citation dialogue box, on the “instant formating” tab.
good luck