Greetings,
The general shape is “rectangular” rather than circular, and a board attached connector is commonly called a “header.” Connector gender is typically reckoned by the form of the electrical contacts, rather than the insulation, so it appears that you’d be looking for something called a “rectangular male header” There’s a product family for that:
There are 4 contacts in 2 rows, on what appears to be something between a 2 and 4mm pitch. The insulation’s black, the contacts are shrouded on all 4 sides, and which is surface mounted at a right angle form factor. Poke those characteristics into the filters, and you end up with a short list of options worth checking into.