Domini canes

It seems that the Order of Preachers have a strong precedent (besides St Dominic's mama's vision) for calling themselves the Dogs of the Lord. From Bede's commentary on Tobit - to appreciate which you need to note that Bede takes Tobias and Raphael as a composite figure of Christ in His human and divine natures respectively:

6:1 Tobias then set off and his dog followed him. When the Lord came to save the Gentiles, holy preachers followed in his footsteps because they carried out what he had commanded: Go and teach all the nations. Finally the Lord himself filled the home of Cornelius with the Holy Spirit and so Peter baptized them with water. On the other hand, the teachers are called dogs because they defend their founder's spiritual home, property and sheep from thieves and beasts, i.e. from unclean spirits and heretical men.

tr. by S. Connolly (Dublin, 1997)