The behavior you described is a consequence of the usage of system stopwords list is correct. This is an expected behavior. "Me" is a stop word, which exists in the system stopword list. System stopwords list used by default by data indexing process.
You can check yourself with this script:
select * from sys.dm_fts_parser('"KA-ME"', 1033, 0, 0)
The third parameter here is stopword list identifier. When you pass NULL, stopwords are not identified on parsing, and you see "ME" of type "Exact Match". When you pass 0 as the third parameter, system stopwords list used, and "ME" will be of type "Noise Word". This means that SQL Server will not save it into the FTS index for searching.
As Raihan mentioned, you can turn off system stopwords list, but as for me, turning off stopwords completely is a too big hammer, especially for Azure SQL Database, because you should pay for additional space (FTS indexes are stored in the same database in the internal tables). Creating a new (smaller) stopword list and use it for FTS may be a better solution.