For transparency and clarity, I want to get a bit more into detail on this (because I can see why you’d want to be able to do it, but want to communicate a bit more about the infrastructure).
The “Send a private message” link is part of the consumer app i.e. twitter.com or the mobile apps, and is translated into the various languages that client supports. There’s no API at all (today) for dynamically modifying the messages or labels the Twitter app puts on these kinds of prompts. Result, you post a link to move a conversation into a Direct Message thread, and it is not configurable.
It would technically be very very complex for this to be implemented as it would potentially require each Tweet with a Direct Message link of this kind to be tagged with some additional ID; have the replacement text somehow posted and stored on the server side; and then for that replacement text to be rendered on all of our client surfaces on every user Tweet impression (and, potentially across many languages). I realise that you’d like this feature, but I hope that by explaining a little more about why this is technically difficult to implement, you’ll get a better understanding of the complexity on the flipside!