Yes, that's the reason you're creating the abbreviation in the first place - otherwise, just write it out in full everywhere.
When you’re defining an abbreviation, write out the words first and then put the abbreviation in parentheses right afterward. Continue to use the abbreviation by itself throughout the document unless you have a good reason to define it again. And don’t get so carried away with abbreviations that your document becomes hard to read.
So your first reference would look like this:
- ... Mr Joe Bloggs (Mr JB) ....
And your subsequent references would look like this (without brackets):
In the event that the person is famous as "Mr JB" but his legal name is "Mr Joe Bloggs", and if you're adding "(Mr JB)" simply to state the connection, then the job of stating the abbreviation is complete at the first mention, and subsequent references can just have: