The word in Revelation chapter 13 for “mark” is the Greek word for a mark of ownership.
Such as a tattoo - perhaps similar to how one marks cattle by branding.
Or how Hitler’s Nazis branded Jews with tattoo numbers for identification purposes.
(below for the thread)
Revelation 13:16-18
King James Version
16 And he causeth all, both small and great, rich and poor, free and bond, to receive a mark in their right hand, or in their foreheads:
17 And that no man might buy or sell, save he that had the mark, or the name of the beast, or the number of his name.
18 Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six.
Revelation 14:9-12
King James Version
9 And the third angel followed them, saying with a loud voice, If any man worship the beast and his image, and receive his mark in his forehead, or in his hand,
10 The same shall drink of the wine of the wrath of God, which is poured out without mixture into the cup of his indignation; and he shall be tormented with fire and brimstone in the presence of the holy angels, and in the presence of the Lamb:
11 And the smoke of their torment ascendeth up for ever and ever: and they have no rest day nor night, who worship the beast and his image, and whosoever receiveth the mark of his name.
12 Here is the patience of the saints: here are they that keep the commandments of God, and the faith of Jesus.
Just a thought, could be wrong, but... being owned by someone doesn’t necessarily mean a tattoo or a mark. If you are owned by Satan it could be by your thoughts and actions, alone.