Using -- Can a mysql user own tables?
There is no "ownership", only permission to read/write/drop/etc.  However, it is possible to have conventions of how permissions are GRANTed that sells a lot like "ownership".

Admin (typically 'root'):

GRANT ALL PRIVILEGES ON *.* TO root@...


"Owners":

GRANT ALL PRIVILEGES ON Leslie_database.* TO Leslie@...
GRANT ALL PRIVILEGES ON Dana_database.* TO Dana@...


That lets Leslie do everything with Leslie_database, but he/she cannot touch Data_database.

Note that the syntax schema.DBO.tablename does not exist in MySQL, only dbname.tablename.

Close enough to "ownership"?

GRANTs can also be done at the "table" level, and even the "column".

You could let Leslie "see" Dana_database:

GRANT SELECT ON Dana_database.* TO Leslie@...