The word integral has several meanings: (1) "essential to completeness," (2) "composed of integral parts," (3) "lacking nothing essential, entire," and (4) "being, containing, or relating to one or more mathematical integers."

Since Integral is one of the main characters in Hellsing, her presence is obviously essential to the story, and this interpretation fits with the first definition. The second and third definitions are similar - it can be argued that Integral has all the necessary characteristics and traits needed to lead Hellsing and to survive on her own. The fourth definition does not apply.

Integral is derived from the Latin word integer. One of the feminine forms of integer is integra, which is Integral's nickname. Some definitions of the Latin word integer include: (1) "complete, whole, entire, intact; fresh, sound, unexhausted" (2) "in quality, [unspoilt, pure, fresh]; morally, [innocent, uncorrupted, pure]; in thought or feeling, [balanced, unbiased, impartial]; of matters for discussion or action, [unprejudiced, undecided]" (3) "renewed, begun afresh".

Although the first meaning is somewhat similar to meanings of integral, the second meaning offers some new interpretations of Integra's name. Although Integra is a virgin, integra relating to morality or thoughts is also interesting. Although Integra is definitely biased (especially against the Vatican and the undead) and has specific, set thoughts, morally, she does seem motivated by pure feelings, emotions, and beliefs. She's not innocent, although she is inexperienced in a lot of things, but in some sense, she is pure.

Wingates seems to simply be an English name.

Hellsing originates from Dracula's Abraham Van Helsing, of whom Integral is a descendent. Interestingly, the booklet that comes with the first Japanese Hellsing DVD also states that "Hellsing" is an acronym for "Her Royal England Legions of Legitimate Supernatural and Immortal Night Guard." That's pretty self-explanatory, I think.

Definitions from Merriam-Webster Online and Latin Dictionary and Grammar Aid.