You have the schemas backwards.
Change...
ALTER SCHEMA MySchema TRANSFER dbo.TableName
...to:
ALTER SCHEMA dbo TRANSFER MySchema.TableName
See a related SO answer for confirmation where the source and target schemas should be in your ALTER SCHEMA
statement.
If the ALTER SCHEMA
statement still does not work, then you have another issue (e.g. you don't have necessary permissions).
For any permissions issues you may bump into, refer to TechNet's ALTER SCHEMA
reference, specifically its Permissions section, which says:
To transfer a securable from another schema, the current user must have CONTROL permission on the securable (not schema) and ALTER permission on the target schema.
If the securable has an EXECUTE AS OWNER specification on it and the owner is set to SCHEMA OWNER, the user must also have IMPERSONATION permission on the owner of the target schema.
All permissions associated with the securable that is being transferred are dropped when it is moved.