What do you call servo connectors?
These are known as "HEADERS &amp; RECEPTACLES" TE calls it as a AMPMODU MTE series.
can be found below at Digikey

3- Pin :-

Header:- 5-147278-2

Plug:-5-103960-2

4- Pin :-

Header:- 5-147278-3

Plug:- 5-103970-3

If you need the header with more pin, just play with the last digit of the above header part numbers for example if you need 5 Pin header connector change the last digit of 4- Pin of header part number from 5-147278-3 to 5-147278-4