Can not be Orlov or the St. Anne order. The Order of St. Anne was not created until 1735, so 'if' painted in 1714, its too early. Grigori Grigorievich Orlov was not even born until 1734. The heraldic crest is close to Orlov, however not exactly a match, their should be two lions rampant in each quadrant, and a few other minor differences.
Sorry I can't help more, but there are those here far more knowledgable than I am on the subject of 18th century heraldry.
Just saw this posting and these are my INITIAL reactions (I will gladly stand to be corrected in any and all circumstances) and I offer these for consideration:
I agree this is not the Russian Order of Saint Anne. The depiction of the seated frontal (and sceptered) Virgin and the way in which she holds the Child is more traditionally reminiscent, IMO. to that of European (non-Russian) origin. My first guess would be "German," taking into the consideration of all the Germanic kingdoms, duchies, etc.
The peculiar lace rectangular neck "tabs," collar, etc. of the individual do not appear in my eyes to be Russian.
The decoration's neck-piece is apparently highly jeweled and the individual is wearing no other decorations (such as a star of the order, but then again, this neck piece may be ALL that is prescribed for that grade of the order).
Could it be an ecclesiastical order worn by an obviously titled noble (not necessarily an ecclesiastic), or could the neck-piece be an elaborate personal pectoral cross of his own preference?
In reference to the arms: the bicephalous eagle is seen frequently in many coats-of arms. The crown adorning the over-all arms is not the shape of the Russian crown, but the closed arches and the center frontal-facing helm, do indicate a family of significant rank. The manteling indicates to me, that the family/ies' heraldic colors are red and white. There also appear to be two "horned-shaped" items in the crest, that are often seen on "Germanic" coats-of-arms's crests.
Unfortunately, I can't quite tell, but are there halos around the heads of the eagles in those particular quarters? Russian eagles do not carry such, unlike the heraldic bicephalous eagles of the Holy Roman Empire.
Regardless, these are (again) some INITIAL reactions, to be considered/ruled out.
Good luck on your research. Regards, AP.