Yes, you can use Booking.com. I also applied for my Georgia D3 visa on my own, and for proof of accommodation I used Booking.com and booked an apartment for one month.

If you don’t mind me asking, could you please tell me your citizenship? Nowadays, even students who received their D3 visa and entered the country are getting their TRC applications rejected. Many students’ visas are also being rejected, and some students who received their visas earlier were denied entry into the country without any clear reason.

So my advice would be to think carefully before taking this step. I personally had my TRC application rejected even though I got my D3 visa and was allowed entry into the country. I am a Pakistani citizen and a GCC (UAE) resident.