The Service of Holy Baptism has a responsibility for a Godparent, referred to as "sponsor." It does not distinguish that responsibility due to the age of the one to be baptized. I have chanted at baptisms in a GOAA parish for 35 years and have never seen a baptism of an adult without a Godparent. An adult will also respond to the priest's inquiries (Do you renounce Satan..., Have you accepted Christ?) along with the Godparent. The certificates from the metropolis also have places for the signature of the Godparent, referred to as a sponsor.
I think Reply #8 is correct about the misunderstanding. One who is received into Orthodoxy by Chrismation, whose baptism was Trinitarian, with water, would be commonly received in North American Orthodoxy by Chrismation; (not so with traditionalist jurisdictions). The Holy Orthodox Churches in the Old World, do not commonly accept such baptisms, including the Church of Greece, from what I understand. This could account for the Godmother's statement noted in Reply #1 above about how she would be perceived in Greece.
Chrismation is a prayer within the Baptism Service, which includes the anointing of the illuminated one with Holy Chrism, "This is the Seal and Gift of the Holy Spirit." When Chrismation is done aside from the Sacrament of Holy Baptism, practice varies among jurisdictions and within jurisdictions as to what else is appended, like recitation of the Trisagion Prayers and the Symbol of Faith. I think the ROCOR also includes a renunciation of previous erroneous beliefs. The metropolis' Chrismation certificates provide for a "witness" signature.