What is common practice for labels of the bug severity?
What is the most common labels for the bug severity: High-Med-Low-etc., A-B-C-etc., 1-2-3-etc. or different? Where they origin? What is the best practice to use?
A label is just a label.
It is far more important to understand what stands behind them, so people can easily say when to assign a certain severity to a bug and understand what such severity means in terms of business impact. This is important because depending on the severity* your stakeholders may take appropriate action. E.g. stop releasing the product or postpone fixing the bug.
For instance, we define Sev 1 when whole system is not working because of the bug, and Sev 2 when only one of the important features is broken. We usually do not accept Sev 1 and Sev 2 in the release, while Sev 3 requires further discussion.
*Obviously, this is simplification. Severity alone might not be enough to take an informative decision, so other parts of bug report can help decide.