My first thought (from the UK) would be Interest-free Installment Plan (see this home-furnishings company1, although they also "brand" it "Flexi-pay"). Variants include Interest-free Payment Plan (see this way of paying for accountancy studies or Interest-free Repayment Plan (see this "Sun" article about an offering from NatWest bank).
The terms above are all generic, and I suspect most people (at least in the UK) would understand them2. However, in this age of "brand marketing", many companies are trying to create their own "catchy" name. There is the "Flexi-pay" mentioned above; others – from companies providing pre-packaged installment plans to merchants – include "Slice it." and "Splitit".
1 All links were obtained from web-searches as examples of applicable terms. I am not affiliated with, nor do I endorse, any of these companies.
2 They will certainly understand that they have to pay less per month, and the "free" means they don't appear3 to pay any more for the privilege. Sadly, far too many people overlook that they will still have to pay the full price in the end, and think these plans make things "more affordable" than they really are. They end up buying far too many items at "only £20 per month"... until they miss payments and get hit by interest charges (see below). [Climbs off soap-box... sorry].
3 Of course, as any seasoned PF&M-er knows, and @RonJohn mentions in his answer, there ain't no such thing as a free-lunch. Either the prices are raised to cover the cost of finance, or the penalties for missing payments (e.g. back-dated, high rates of interest) are swingeing. Or both.