What you call yourself, what your family and friends nickname you, and how you are addressed in social settings and work tell others about who you are. Specifically, nicknames should never spill over into social situations – especially around people who are important to you or your career. Of course you may experience the ragging by family and friends when a new friend or potential mate is introduced, and how the new person reacts will let you know if it is acceptable for them to adopt the nickname.
And whether people pronounce, attempt to pronounce, or ask the correct pronunciation of your first and/or last name tells you about who they are. But if there is no consideration for that pronunciation at all, do you correct them or let it slide – because that shows how much respect you have for yourself. It is not arrogant to correct someone about how your name is pronounced.
The worst faux pas is when someone gives you a totally wrong name – maybe by mistake or maybe intentionally. If it is intentional, it shows that you are not regarded at all. And how you respond to the mistake makes a world of difference – you are seen or not seen as significant enough for your name to be remembered. This is particularly important when in a work environment. Your boss should know who you are for obvious reasons, as well as your coworkers. But if anyone chooses to call you by another or mispronounced name, then it shows that you are no more than a cog in the wheel and not someone who would be considered for bigger and better things or an important member of the team.
It is up to you in all circumstances to correct others or demand that the nicknames stop. It’s all a matter of respect.