Sadly, IT systems that can't handle apostrophes are real. Since the character is used for both contractions and for quoting, it's easy for real-world software to mis-handle it. Worse, if accepted as data input and not handled correctly, it can be used for data-injection attacks on backend systems, so a lot of security departments agitate to block it at the front end. Yes this is all very frustrating but it's very much the current state of affairs. A year ago the local gov't hired some outfit to cobble together a database to organize covid shots for employees in our sector of work, and guess what, it choked on apostrophes, which until that time had worked fine in our systems. Do they suck? Why yes they do, but if we wanted our staff to get their appointment notices, we had to assign them all apostrophe-free aliases. So we did.
And that's the obvious answer: for the company to assign you an email address (and login name etc) that comes as close as possible to your proper name, that works in their systems. This is bog-standard for names too long, too hyphenated, too accented or too apostrophe'd to work. It's very common for Juan Esperanza D'Souza-Rodriguez to end up with the email address juan.dsouza@company.com.
The idea that someone should change their real-world name is absurd, and as others have hinted, may be a joke, or the brainfart of a very misguided low-level IT operative. Not to be taken seriously.
Now, if your company is super rigid about this and proposes to change your name in their records to remove the apostrophe, so that you are consistently ONeil or OMalley or DSouza throughout the company, you might need to go along with it. I'm known to my (large bureaucratic and highly-regulated) employer as a short form of my legal name (think Mel instead of Melvin) and my bank is happy to deposit my pay, the govt happy to take my taxes, etc. IANAL but I'm very much under the impression that doing business in good faith under a variant or minor mis-spelling of your real name is absolutely no issue, unless you try to use it fraudulently, like to escape tax or double-dip on benefits. So if they propose this, it's probably the way to go.
