what is the name for this DC connector?
Rev A

It's called a DC POWER JACK but in the category of  barrel-power-connectors . which normally have a sleeve switch  "sleeve=outer conductor" with output on the side pin. Normally today 0V return path is on outside and +V is on centre pin. So we might call this application a low side SPST or sleeve switch with 3mm center pin and 5.5mm diameter sleeve male receptacle.  Although we do not use the sexist term male and female for (floating) plugs and (fixed) jacks anymore, we prefer to call them Plugs and receptacles for mechanical reasons.  But for limiting exposed power, connectors are usually "pins" for the electrical load receptor and "Sockets" for the electrical source while connectors  termed "Jacks" are simply Fixed mounting connectors and Receptacles refers to the electrical connection. But unlike AC outlets, it is both an electrical and mechanical receptacle to receive a plug which takes the electrical load.

Some DC barrel connectors are explicitly defined in sort columns such as at  Digikey under Internal Switch as "Does not contain switch" but these are the exception.

However, Digikey and others carry no stock.
credits to @Passerby for the nudge on "all"

Other Mfg's describe it as JACK, 2.5MM PIN, SHORT BUSHING

Connector names should be abbreviated in BOM's with description in reverse order of significance, thus a common abbreviation is simply.

CONN PWR JACK 2X5.5MM  SWITCHED SOLDER

However many major connector factories find  define any connector with (M) or (F) which I support as being easier to understand especially when users have the acronym as effective series inductance. (ESL)

 UPDATE

Not all pins are the same diameter, and this is critical for good contact.
ALthough I said 3mm and 2.5 this was a generic size THere are many others.

prompted by comments @DanDavis and @Passerby (keep up the good work)

I looked up the website in the photo
Now that you know how, dont ask again.

The part number and description is DC-005 5.5-2.1MM 2.0 Power supply DC  but generically it is a CONN, Barrel, DC 5.5mm-2.0mm ( I suspect the difference is the pin and socket diameter of the center conductor

http://www.xinlgo.com/product_detail-1850.htm