why do the english use the french name "Broderie Anglaise" (translates as english embroidery).
and did it have a name in use before the french version was adopted?
It originated in England in the 19th century and became very popular in France, who coined the term which then transferred to the rest of the world, including England. This is not particularly unusual, cf 'redingote'.
Prior to that, it was probably known in England just as 'embroidery'...
Probably because it is a term used in French dressmaking and sounds much 'posher' than the normal English. For the same reason the term 'cuisine' is used rather than the more prosaic word 'cooking'. Which looks more appealing on a menu, "Prunes sèches à la crème anglaise" or "Prunes and custard"?