Madeleine:

When you receive an e-transfer do you not receive an e-mail notification from the bank that states you received an amount of money? If so, why not have the client add an invoice number or apartment number or address or name in the comment field before they send their payment by e-transfer.

One really low-tech way to solve the problem is to make the rents all different.  One client of mine did this by adding the unit # - in pennies - to the rent.  So unit #1 had to pay $500.01 of rent, unit #99 had to pay $500.99 of rent.  There are downsides - you're asking for (a tiny bit) more money from your tenants, you have to figure out what to do with the extra money, etc... but it does solve the problem of figuring out who has paid.

(Our client takes the extra $ and puts it into a fund for buying treats for the tenants.)