New accounts start with a short BlueMail signature, and it is yours to remove or replace. Signatures are set per account, so a work address can carry your full details while a personal one sends nothing at all.
Go to Settings | Signature, then choose the account you want to change.
Turning It Off Completely
Switch Include Signature off. Nothing is appended to your outgoing mail from that account, and there is no text to clear.
Replacing It With Your Own
Leave Include Signature on, tap into the signature body, select the default text and delete it, then write whatever you would like to send instead and tap Save.
The default reads Get BlueMail for Mobile on a phone or tablet. On a computer it names the platform you are using, so it appears as Get BlueMail for Windows, for Mac, or for Desktop on Linux. Whichever you see, clearing it works the same way.
You can keep more than one signature and mark one as the Default, which is handy when you write in more than one capacity from the same address.