All our accommodation is booked in the name of one person. My name is
nowhere in the hostel or hotel receipts. How do I show these receipts
as a proof for my accommodation?
Unfortunately this means you do not have proof of accommodation. You can show his proof of accommodation and your communication (emails, for example) where he promises to accommodate you. However technically this is not proof - because he could have sent the same email to twenty other people, or could have sent you a follow-up saying that he's not going. Immigration has no way to check any of those, and they require "Truthfully notify the verifiable places to stay in Thailand" as part of qualification for VOA.
Also consider the possibilities: what if this person holding the accommodation is denied entry to Thailand? What if he/she gets into accident on their way to hotel? This would leave you stranded.
The link says that I need a travel plan. Is it like a travel itinerary? Should I just write a document about the places I am visiting?
Travel plan is more like an overview of what you're going to do and where - and of course it should match your proof of accommodation and other evidence. For example if you plan to stay 3 days in Bangkok and 3 days in Phuket, you may be asked to show tickets to Phuket and hotel reservations there. Tourists visiting a country usually have at least vague idea how they'd be spending time there and where. There is no need to provide a timesheet document with exact dates and times, or any document at all - but you must be able to answer questions about how you are going to spend your time in Thailand, and match it with other evidence.