Shelly Zeitlin wrote:

You wrote recently about the reason for using two Yuds as a substitute for writing the Name of Hashem. I've heard (no doubt from Rabbi Moshe Meir Weiss of Staten Island) the following reason: Yud is the only purely 'spiritual' letter, i.e., it is written entirely above the line. Two 'Yids' (Jews) together, side by side -- both spiritually engaged, experience the presence of Hashem. [This idea is expressed in the verse "Love your neighbor as yourself, I am Hashem (Leviticus 19:18)." When there is love and respect between two people, Hashem's presence can be felt. - T.R.]

Binyamin Yaakov Schwartz wrote:

I heard not long ago a different reason from my father in Boca Raton, Florida. He told me that the siddurim used to abbreviate Hashem's Name by putting two yuds together, with a small letter 'vav' lying horizontally on top. The reason was that the numerical value of two yuds plus one vav equals 26, which is the same as the numerical value of the Name of Hashem.

Sources:

• See Melamed Hatalmidim L'Rabeinu Yaakov Antoly, p.118