I used to have my texts set to automatically add my name after every text. I know this was done via the my rogers app. I recently moved to another carrier and lost that function. Then with the sweet deals of late I was enticed back to rogers and for some reason I cannot find this function anymore. It was so nice to have because people who did not have me in their contacts knew who texted them.
This sounds very similar to the Rogers Extreme Messaging service -- unfortunately Rogers has decided to cancel the service in January 2018 - while those who had it, get to use it up-to that day, new customers and/or changes to the service cannot be made.
I'm very disappointed in Rogers for discontinuing this product, that really costs nothing to offer. For me, since I work outside of cellular a lot of the times, I had it setup to send an email copy of my text messages -- I would be able to see the message and then act as needed. It was also handy for traveling -- since it was server based, while say traveling by plane, I could view (at almost real time) text messages coming into my inbox -- all while my phone had no coverage and was off. Can't do that with an app on your phone.
As for your request of personal signatures, that too was part of extreme message - sucks you returned under the assumption it was still available. Extreme message was that feature that Rogers had no one else does. Even if used by very few, it was cheap to operate and it kept customers because they knew it wasn't available.
While I haven't been able to replicate what I need (off phone text to email copy) and never will unless a carrier offers a similar updated service -- with personal signatures, I'm sure there is a shady, app in the Play store (Apple too, but that's more restrictive for developers) that would be able to add stuff like that.