Point 4 on the following gives the Revenue official line.
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If you want to be absolutely correct especially with large invoices then make sure your business is properly titled on them as per the legal requirement especially going forward.
As I said earlier however, I have never, in 24 years or dealing with Revenue had a VAT auditor disallow an invoice from a claim because the purchaser's name was not on it. Other verification procedures, such as cross checking to your cheque payment can be used to verify it was correctly yours.