No.
Finnish law does not oblige a private trader to obtain a business account. Of course, for the entrepreneur's own financial management, it may be wise to set a separate account so that the company’s incomes and expenses can be easily seen from the same place, without other personal money transactions confusing the view. However, a private trader doesn't have to have a business account, but a standard current account is also suitable for this purpose.
The UKKO Entrepreneur service is not linked to a business account, so the service can also be used by entrepreneurs who don't have a separate account for the company, and the business's incomes and expenses are easily kept in order when you remember to always add them to the UKKO service.