At first glance, I would guess that your name is some kind of variation of "Arthur". Perhaps a recording clerk had misheard the name "Arthur" and that was how you'd wound up being named "Arter"?
Alternately, you may have been given the surname of "Arter" as your first name. Two English surnames which contain the element of "Arter" are "Arterberry" and "Arterburn".
"Arterberry" is a variant of "Atterberry", and means: "One who came from Attenborough (the fort of Eada's people; or of Edda), in Nottinghamshire; or from Adderbury (Eadburg's fortified place), in Oxfordshire."
"Arterburn" means: "One who came from Otterburn (otter stream), the name of places in Northumberland and the West Riding of Yorkshire."