I believe there is a long, administrative process, where the would be bearer must journey to Terra, and beseech the High Lords to change it. The alternative is that, since NO ONE may countermand the orders of the Emperor, a Warrant with no applicable bearers would simply be nulled, and stored in a file on Terra. If Steve wants a Warrant, and is found worthy, they'll make him a new one, riddled with the controls later snuck into the Warrants to make the RT slightly manageable. They aren't made out of anything special, such as Unobtainium, so it's no more work to write up a new one, and almost guaranteed less.
This statement sort of moots some of my own story/commentary, earlier. If the Warrant must be hereditary, then no one else can get it, just another one, and work to eat up everything the previous Warrant owned. If the bearer can name successor, and it needs not be family, then the new RT would get the Warrant, and, if his name is different, the prior might be able to request that the Warrant be edited, which is less a slap to the Emperor's face. Otherwise, just adopt the newbie, and they must accept that the Dynasty has a different name; this saves on getting all the towels remonogrammed, anyway, and capitalizes on the name recognition already present in said Dynasty.
This is partly why I wanted my Dynasty to be the Silver Ravens, rather than House ________, which became House Korvallus in 708.M41. If Korvallus has no children (and at around 300, I don't expect him to start the practice this late), and the Dynasty is known by the Company name, rather than House X, it would be easier to appoint one of his cultivated Lieutenants to succeed him, without all the hoopla of changing the Dynasty's name, or the Lieutenant's given name. Oh well, I suppose bits of this are the kind of stuff we just say "the GM says…", and let it work. GW isn't likely to show up at my house, and beat me with the new TT core book because I oopsed a bit, or slightly altered, their "established" canon.