It's called the anus guys, and it's the acceptable medical word
Yes, doggy style can be for anal sex or vaginal sex.
Sex when standing is harder than when lying down or with her on her hands and knees. Her anus is likely to be very tight when she's standing and that would prevent entry. Try it laying down or "doggy" style first.
Use a ton of lube!! You hear me? Don't put your penis anywhere near her anus until it's soaked with lube, and she has lube on her anus too. Anal sex can very easily be painful unless you do it right!
Take it slow. Really, really slow. I advise sliding in one finger until she's used to it, then two fingers, and finally three fingers. Once you can fit in three fingers, you'll likely be able to fit your penis. She's got to be relaxed or it will never work.