Śatapatha Brāhmaṇa ("of a hundred paths") 4.1.2.2

4.1.2.2

atha yasmādantaryāmo nāma | yo vai prāṇaḥ sa udānaḥ sa vyānastamevāsminnetatparāñcam prāṇaṃ dadhāti yadupāṃśu gṛhṇāti tamevāsminnetatpratyañcamudānaṃ dadhāti yadantaryāmaṃ gṛhṇāti so 'syāyamudāno 'ntarātmanyatastadyadasyaiṣo 'ntarātmanyato yadvainenemāḥ prajā yatāstasmādantaryāmo nāma

Now as to why it is called Antaryâma. That which is the out-breathing is also the in-breathing and the through-breathing. Now, in drawing the Upâmsu (graha), he puts into him that out-breathing which tends away from him; and in drawing the Antaryâma, he puts into him that in-breathing which tends towards him. But this same in-breathing is confined within his self; and because it is confined (yam) within (antar) his self, or because these creatures are sustained (yam) by it, therefore it is called Antaryâma.