I also use eRentPayment and have for the last 1-2 years. Customer service is really good and responsive to tenants that need help, and their bounced payment fee is only $2 - nice to see a company not overcharge for something like this, as banks have forever.
I have not seen the tenant name appear on the payment, though. In fact, I have had some situations where two payments were made on the same day and the deposit lumps them together into one payment, without either name mentioned. I can figure it out from the payments in erentPayment itself, but I would imagine if I had dozens of units on a single account then it would be impossible to determine by just looking at the bank statement.
The set up for eRentPayment can take a few minutes and offers MANY options such as not allowing partial payments, requiring previous month rent be paid before accepting rent for current or later months, allowing additional payments for items such as utilities or deposits, etc.
Did you do anything special to get the names to appear? I don't remember anything in the set up.