I have the membership pass but have loss it. Can they check for our active membership period with just our names?

I just did that. They will let you in with photo id matching the membership names. They will even give you a temp to get your usual discounts.

Also i believe they check name and ID cards - like license...

If you paid with anything other than cash you will have proof of payment, keep the proof available when you make your request to issue a duplicate membership pass.