When executing function =MONTH(NOW()) the result should be "3", but, I get
The month today is March 2021.
No repro in
Version: 220.127.116.11.alpha0+ (x64) / LibreOffice Community
Build ID: d8ed3bda462b351d2b98ec57cfdb879e0eec0010
CPU threads: 4; OS: Windows 6.1 Service Pack 1 Build 7601; UI render: Skia/Raster; VCL: win
Locale: ru-RU (ru_RU); UI: en-US
I got 3 as expected
The MONTH() result *is* 3 but you can't format that result as date and expect it would display March, same as with any number 3. Instead, it displays the date for "3 days since null date", which for the null date 1899-12-30 happens to be 1900-01-02 so for your MMM-YY format you get Jan-00.
Just use =NOW() and format it to MMM-YY if that is what you want.