I've seen a few of these records and yes, there are names telling who paid for things.
There are four pages (pages 117-120) about these records in the 2002 edition of Cradled in Sweden. Most of those pages are scans of an example of such a record plus a transcription and a word list. This comes before that.
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Parish Accounts (Kyrkoräkenskapsbok)
When available, the parish accounts usually go back to the 1600s. They may contain detailed accounts of those who paid for the opening of a grave indicating a death, or who paid the bride's money or gave a special donation at a christening. The donors were usually very close relatives and thus these accounts may supplement some missing parish registers....
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I remember finding some useful information besides accounts in one of these books. I don't remember offhand which parish. There were baptism dates for some children, which was great to know because those birth/baptism books were missing for those years.
Judy