Can I use my studio's name instead of my personal name? I don't want "Rajesh Sharma Photography" mixed up with my actual personal identity everywhere.

Yes, and you should — that's the intended setup. Under Profile & Brand you can set your display name, studio name, tagline, website, address, and your handle, and that's the identity guests see on album pages and on your public profile. You can keep your login email completely separate from your public brand. A lot of photographers run their whole client-facing presence through the studio name while the account underneath stays personal, and Snaptide handles that cleanly.