Thanks for your question.
I take it your are referring to Revelation 19:16.
We must remember that this book is a book of symbol and if we look at the use of "thigh" symbolically in scripture it is very instructive. In Abraham's day, a covenant was confirmed by the placing of the hand under the thigh of the one confirming the oath [see Genesis 24:2,9]. Jacob's thigh was damaged by the angel to teach him to rely on God and not on his own strength [see Genesis 32:25,31,32]. Psalm 45:2 depicts the conquering Christ
with his sword upon his thigh. By this time in Revelation the "Lamb of God" is revealed as the "Lion of the tribe of Judah" riding forth to conquer, not in his own strength but by that of the God of Heaven. The covenant, once ratified by the blood of the lamb, will be sealed and fulfilled in the power of God as His son fills the earth with His glory.
I take it that the name was written both on the robe or cloak and on his thigh, either in the flesh of his thigh or on the garment which covers it. However, Revelation is a book of sign and symbol so this is not to be taken as a literal "tattoo" just as in Revelation 19:21, the sword coming out of Christ's mouth is not literal but rather figurative of the word of God.