I took the name from the Ebony. It can be viewed in some pictures of the 1st game as well.
To be precise it says "For Tony Redgrave by .45 Art Warks". Of course this doesn't make much of a sense.
After a research I did, I arrived at an info that Devil May Cry 1 was supposed to be Resident Evil 4 and thus Dante was Tony Redgrave. But still no clue about the "Art Warks".
The research thus continued until I found the details of the 1st Devil May Cry Novel. It is not cannon anymore but when it was, it featured the events just before the 1st Devil May Cry, as we see a girl (probably Trish) arriving at the shop at the end of the novel.
In that novel, Dante is part of some Devil Hunters.Because of some reasons unknown, probably trying to hide his relation with Sparda, Dante uses the name Tony Redgrave. Enzo Fearinoh is the one who gives them jobs. And Nell Goldstein is a gunsmith from who some of the Devil Hunter's gain their weapons. Dante's power makes almost every gun break after a while, so he goes to visit her regularly, although he usually is broke. The shop is named ".45 Art Warks" and because Nell, likes Dante, since he reminds her of her grandson, and so decides to make some really durable and easy to use guns that will last.
After some events Dante gains Ebony & Ivory from her (Ebony & Ivory being the title of her favourite song) which featured the words "For Tony Redgrave by .45 Art Warks".
Hope I explained correctly, since I don't known the novel, and I haven't read it myself.