Can iPhone X be activated without a second line?

Your question isn't very clear. If you're planning on using the new iPhone X on your current number, you don't need a second phone number. If you want an additional line of service, that's something you should discuss with Verizon.

If you're talking about getting the code for two factor authentication, no, you can have the code sent to another trusted device of phone number.

Two-factor authentication for Apple ID - Apple Support

If you mean something else, please explain.

No. You need one phone, one number and one carrier. I'm not sure I fully understand your question, but if you are unsure how to activate your phone on your number, contact your carrier and they can activate it on their system, using your IMEI and CCID numbers, which you can find in Settings > General > About.

Why would you need a second phone?