There's a world of difference between ingratiating yourself by having yourself and your family painted into an icon (all of whom are alive), and showing two saints (Justinian the Great and Constantine the Great) supplicating before Christ.
If you can't tell the difference between deference and self-promotion ....
Justinian was alive when Hagia Sophia was being built. There is also a handful of others.
He might have commissioned the church while he was still alive, but churches of that size and scale take decades to complete. The church was completed well after Justinian the Great's death, including the mosaics, by his successor.
I repeat: The iconographic depiction of Sts Constantine and Justinian, both holding models of churches, supplicating before Christ, is completely proper, and something seen in countless icons of enlightener-saints, equals-to-the-apostles, and sainted founders of churches and monasteries. OTOH, the painting of the businessman and his family members in an otherwise proper icon of St Nicholas Help of Mariners
, is blatant and blasphemous self-promotion. The iconographer who painted this schlock should also be taken to task for painting it. It is a betrayal of basic principles.
The proper way to indicate patronage of a church is to have one's name on the honor board which is hung in the narthex. Patronage of icons is ideally done anonymously, but, if a patron "must" be commemorated by name, then this should be done as a discreet painted inscription in a lower corner of the icon, and with lettering small enough that the inscription would be legible only at a very close distance. The emphasis must be on the icon, and the holy one(s) within it, not on the identity of the patron.