short answer, No they can't "Snoop" your computer. They can't look at your files or see what your work is about etc.
Honestly if privacy is your greatest concern don't use any other software than what your company deems acceptable on your workstation. (and even then companies can recommend some shady software)
Who's to say your work isn't spying on your computer? <- sorry tinfoil hat
Your computer's name is not a secure piece of information. It's practically a username for every piece of software you run.
If you're still deeply concerned, Learn about Virual Machines and run it in a fresh windows VM. That will alleviate much of your concern but please note that you still need to follow the P99 rules.
And we can't assist you in how to set that up. There are plenty of guides/tutorials online for legitimate use.
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