Could you please send me part or ORMD1 model where this association is defined? There is probably some problem in conversion self-MN relation from v1 to v2 project.
Regarding to your first sample, these are results I currently get:
Model:


When alias is defined for inverse entity schema is correctly exported:
Acme\DemoBundle\Entity\SampleEntity:
type: entity
fields:
id:
id: true
type: integer
generator:
strategy: AUTO
name:
type: string
length: 255
nullable: true
manyToMany:
Parent:
targetEntity: SampleEntity
joinTable:
name: Sample_Parent
joinColumns:
sample_entity_first_id:
referencedColumnName: id
nullable: false
inverseJoinColumns:
sample_entity_second_id:
referencedColumnName: id
nullable: false

When alias is defined only for owning side, ORM Designer export only partial definition of many to many association:
Acme\DemoBundle\Entity\SampleEntity:
type: entity
fields:
id:
id: true
type: integer
generator:
strategy: AUTO
name:
type: string
length: 255
nullable: true
manyToMany:
Parent:
targetEntity: SampleEntity
mappedBy:

If both aliases are defined, my schema now looks this:
Acme\DemoBundle\Entity\SampleEntity:
type: entity
fields:
id:
id: true
type: integer
generator:
strategy: AUTO
name:
type: string
length: 255
nullable: true
manyToMany:
Child:
targetEntity: SampleEntity
inversedBy: Parent
joinTable:
name: Sample_Parent
joinColumns:
sample_entity_first_id:
referencedColumnName: id
nullable: false
inverseJoinColumns:
sample_entity_second_id:
referencedColumnName: id
nullable: false
Parent:
targetEntity: SampleEntity
mappedBy: Child
All these definitions looks correctly. It's possible that we fixed something when we searched for bug or we're missing something.