I'm trying to be this part separately but I don't really know its exact name therefore I couldn't find it.
It's the black separators highlighted in the red rectangle that I'm looking for.
I tried looking for pin separators and pin spacers but that didn't result in anything.
Best Answer
As mentioned, these spacers are not sold separately (not as a standard part, anyway). However, you can buy headers just like the one you showed in your first picture with the spacers already added. I know Sullins sells some connectors like this with the option of adding these spacers within the order. It's part of the part number configuration. See the catalog page for the PPPC series (http://sullinscorp.com/catalogs/101_PAGE114-115_.100_FEMALE_HDR.pdf). In the fourth table on the first page you'll see the different options for spacers and tail length. I think this is probably what you're looking for. The top of page 2 shows how to configure the part number.