でいらっしゃるis, are (respectful, of a person)

Before it

A name, a title or a job. Or a な-adjective about them, usually with お: お元げん気き, お好すき.

Said about

The person you are talking to, their family, or someone you both look up to.

Where you'll meet it

Staff checking your name at a counter or on the phone, introductions, speeches, polite letters.

In use

Who is it about?

Respectful forms raise what the other person does. Humble forms lower what you, or your side, do. You never raise yourself, and to an outsider you never raise your own family or company.

でいらっしゃる is respectful: the same いらっしゃる as the respectful go, come and be. It is about the other person, so you answer without it.

はい、山やま本もとでいらっしゃいます would raise you.

でいらっしゃる or でございます?

Both are です made more formal. でございます only makes the sentence more polite: it is for things, for yourself and for your side. About the other person, the careful choice is でいらっしゃいます, which raises them.