I would like to know how to invoke Babaji’s blessing and presence with me to reach the level of samadhi in meditation. Can I repeat his name as a mantra to invite him?
Paramhansa Yogananda answers this very question in his Autobiography of a Yogi in the chapter, Babaji, Yogi-Christ of Modern India. He quotes Lahiri Mahasaya as saying, "Whenever anyone utters with reverence the name of Babaji, that devotee attracts an instant spritual blessing."
To use this technique to attract spiritual blessings is a good beginning. But to achieve a level of samadhi requires great self-effort on our part. We need not only the blessings of Babaji, but also our regular, ever-deepening and heartfelt effort in meditation.
Through daily meditation we can begin to attune our consciousness to Babaji’s. It is also important to keep the attitude of self-offering as the goal of each meditation. In other words, it’s important not to meditate to "gain" something (even the state of samadhi!) but to offer ourselves, especially our ego identification, ever more completely into the divine light.
As a great saint of the west said, "It is in giving that we receive."
I would also recommend that you read and meditate on this chapter on Babaji in the Autobiography of a Yogi. I think you will find deepening inspirations from doing so.
In divine friendship and joy,