I like the idea of having the name of your love tatooed. I think,it is a little sad, if the tatoo is no more than an expression of ownership or submission (but I guess a sub might see that different) , but if it displays the name of a true love, it is a very romantic thing. So if it shows not only your submission and ownership to your dom, but also the dedication of your heart, I could not imagine a better gift for your partner.
And just to say my part to the topic... I love the look of rope marks on a beautiful woman...
Btw: I would be very careful when trying to leave marks, because they can really get worse with time. I once had a night with a girl that bit my arm and although the bite marks did not show immediately, they became huge bruises the day after. Just keep that in mind, I guess it would be pretty embarassing if the nice looking rope/bite/whip/gag marks turn into deep blue bruises that can be seen from miles away for the next two days, especially if you have to go to work with them.