Is It Okay to Reveal Company Name or Share Offer Letter During Negotiation?

I’m currently in the middle of salary negotiations and had a quick question:

If HR asks which company gave you an offer, is it okay to reveal the name? Can it cause any issues?

Also — what if they ask you to share the offer letter? Is it normal to provide it, or can I refuse?

Lastly, is it possible or common for one HR to contact the HR of the company that gave the offer to verify?

Would love to hear your thoughts or experiences.