You dont have to match your Ebay account with your Paypal account,some Ebay sellers sell for others,and prefer to use their Paypal account to accept payments/
Mismatching names are generally not recommended. The main reason someone would want to have mismatching accounts is they might be trying to salvage an account that was paired up to a previously banned one. This is also not recommended since very often it links back to the old suspended account(s).
The account ID's are permanent and usually shared between PP/EB.