Wedding Invites After Elopement

I would use the name you will being using at the time of the event. People will already know you are married, so why would they think it's weird to receive an invitation from someone with your name that you have been using for a year?

Interesting question.
I didn’t put my last name at all. My parents helped pay so I worded them like this
Mr and Mrs parents with my maiden nAme invite you to the wedding of Cassidy Middle name and husband whole name (first middle and last) So that may be an option if they’re helping pay. If not I don’t think there’s a wrong answer. Maybe
You’re invited to the wedding celebration of you and spouse married name. Since you’re already married and this is the celebration. I hope I helped a little.

If you are already married then this may be referred to as "a post wedsing reception" or "vow renewal."

You may use the name which you are using post marriage. Or avoid the issue and use your first names only. Are you doing a vow renewal, or a reception for the ceremony you already had? Smith-Brown part I wedding ceremony followed by Smith- Brown part II Reception would seem reasonable if you are looking at it that way.

You should put whatever your name is when you send out the invitations. I would find it weird to get mail from someone with a name that they changed a year prior.

Be honest with your guests. You are now married so use your married names. They are being invited to a renewal of vows, not a wedding.

I would use your married name- people know your married. It would be super weird to get an invitation with your maiden name. I’d be thinking “but I thought they got married last year???”

My husband and I are doing the same thing. My name is already changed so that's what I will be putting on the invites.