I'm not an accountant, but as I understand it, 'home office' in the official sense of the IRS is a room or space exclusively dedicated to work, so that its expenses (computer, printer, phone, ink, paper, software, etc.) are deductible as business expenses, whether by people who work as free-lancers or independent contractors or people who run a business out of their homes. If I recall correctly, it can't just be a desk, table, computer, or work area also used for other purposes, like kids' homework or household bill-paying.
So yes, the combination of words exists, but it isn't the same as working at or from home, also called telecommuting, for a particular time, whether regularly for a certain number of days per week or month, or temporarily for a period of weeks or months like now with pandemic lockdowns.
You could theoretically call the latter '(doing) home office,' but to my ears that would sound noticeably Denglish, because it isn't a fixed phrase in the way that 'Home Office (machen)' (?) seems to be in German.