i put my preferred name then my first initial of my birth name. so say my birth name was Stephanie, i'd put S. Bob Smith. i did this when i got my current job and they just asked what the first initial stood for. i explained i was trans and that i was in the process of getting my name change. they said it wasn't an issue. when i had my job interview, no one knew. the only one who knew was HR (AFTER i was hired) and the guy who gave me my interview when i had to fill out the paper work for accepting the position. even on the paper work i put both names. my job has been great about keeping my birth name a secret but now my name is changed, so it doesn't matter anymore. my name tag said my now legal name, male pronouns were used, etc. there was no issues with anything and i'm completely stealth at work.
i believe the only time you need to let them know is when you get hired for paper work reasons, etc. and if you're stealth, i'd explain upfront that i am stealth, this is the name i go by, these are the pronouns i use. if you're in an LGBT friendly country/applying for a job that has anti discrimination laws, you shouldn't have an issue (at least i hope not).