If I gift someone on Steam, will they see my email address?

Yes, they will. Here's the (redacted) start of a recent gift email I got:

Hello,

Your friend s-------- ([email protected]) has given you a gift subscription
to the game Strike Suit Zero Mega Bundle on Steam, the leading digital
distribution platform for PC Games.  Here's how to redeem your gift:

They'll see both your Steam name, and the email address Steam has for you. Note that this message will be sent whether they send the gift through Steam, or tell Steam to email it to you.

You can change the email address Steam has on file from Steam -> Settings -> Account -> Change Contact Email.... You can also avoid revealing your email address entirely by trading it to them directly with the in-chat trading system, although this requires you both to be online at the same time.