Just Deaf or Hard of Hearing is fine as this is much more accepted than another terms like hearing impaired or deaf-mute etc but keep in mind when on official business they usually say hearing impaired as this is what they think of when they first meet you, so don't get too worked up or angry please Deafies.
just say for example... let me show you an example I will use my name ....in a coversation.....
I say
" Hi Good Morning, ma'am I am here for the job interview. My name is Mr. Austin. "
She says
" Good Morning, Let me get Mr. Fruehauf please have a seat. One moment please? "
" Hi, Mr. Fruehauf, There is a hearing impaired person who writes on his own paper and pen he asked for you , ummm his name is Mr. Austin ? "
Mr. Fruehauf says,
" Excellent, bring him in. " as he swivels around in his leather chair.
The secretary comes back and motions with her hand and says
" Yes, you may come in. "
I walk in and promptly thank the secretary and shake hands confidently with Mr. Fruehauf then wait until he sits down then he says, " Have a seat. " as he motions with his hand.
I say " Hi Good Morning Mr. Fruehauf, my name is Mr. Heath Austin and I am Deaf, I communicate by American Sign Language, ( ASL ) and I am here for the job interview, Can we wait until the sign language interpreter shows up please? I am sure the sign language interpreter is on the way here as the interpreter is booked pretty solid and should arrive shortly. " then I look at my watch and I write down that I showed up here on time, ready to work.
then the ASL interpreter shows up and is ready to start interpreting then when done and Mr. Fruehauf says " You have the job. " I say Thank you Mr. Freuhauf then I promptly say Thank you to the ASL interpreter.
( This is an example of a real world conversation, ideally ASL interpreters should show up before the Deaf person shows up but sometimes that does not always work in the real world then you need to have positive stragetries. )