How can I be more robust mentally?

What are the repercussions of the complaint? It should be sorted to everyone's satisfaction and all parties can move on.
People can be very quick to complain and some are rather unforgiving. Please forgive yourself and move on. A different person may not have complained. We're all fallible, your colleague is right, learn from it but let it go - and then you'll grow.

We all walk on the same ground. I guess you have apologised - if not do. Why did it happen? It there anything you can do to reduce the chances of similar in future? I have found sometimes when I'm the object of what seems unreasonable anger - there is some other cause nothing to do with me that has added to the heat. Might that be part of this?

Shoulders down, head up, breathe and smile. You have friends here among the old souls.

You made a mistake in your work. Everyone does.
Presumably you will be conducting similar ceremonies in future, therefore practise and rehearse as much as you are able before each one until your confidence returns.
You can't undo the mistake but you can ensure you don't make it again.

Ooops. Learning from it, not 'earning' from it.

Just remember that we ALL learn through our mistakes.. you won't do it again. stop beating yourself up and see it as a good thing.. people probably didn't even notice.. I bet you wouldn't have given it a second thought if a colleague had done it,,,

We used to have a saying at work 'Please who aren't making mistakes aren't doing very much'.

The whole of life is about making mistakes, correcting the mistake where you can, earning from it and moving on. And hopefully not making the same mistake again.

Take a deep breath, head up high and carry on.

I run a business and sometimes I inadvertantly get peoples names wrong as I sell worldwide and some of my customers have challenging names. If they complain I just say Im sorry you were upset, this was human error and no one is perfect.

Then I just move on past it.

Women (so I am told) tend to beat themselves up for errors. However men compartmentalise things as a protective mechanism so they move past mistakes more easily.

I'm so sorry you have a useless manager, a good one would reassure and I'm sure you have apologised.

Sometimes a chat with your union rep may help, not to make a big thing out of it but to reassure.

I suppose just triple check next time. Nowadays I think it is the solution you find to over come your mistake that counts. As they say nowadays, if you take ownership of it, it shows a robust approach.

Take some time off. Work on getting some perspective and try to speak compassionately to yourself.

This is what I tell people on my team, it might help?
Try to maintain a positive perspective when it comes to mistakes at work. It's important not to panic over small issues. With only a few exceptions - making work-related mistakes won't end in a life or death situation.
Many mistakes are resolvable immediately or soon after the error occurs.
Take accountability for the mistake and try not to make excuses for why the mistake occurred, apologise and make a plan for next time!
We've all been there at some point!

Were marrying not we’re, predictive text gremlins.

You say you got someone’s name wrong in a ceremony.
If you are a celebrant and we’re marrying two people and got a name wrong then that’s pretty poor and upsetting for the misnamed person.
Same for a funeral or christening.
Can you explain ‘ceremony’ to give context.

Who complained? The person whose name you "got wrong" or someone else? What exactly do you mean by "got wrong"? – mispronounced it? or mistook them for someone else?

Was this an Oops, sorry! sort of slip or did you implicate someone in an evil deed?

You do know beating people up in itself is very wrong, I trust?

Sounds as if your friend who tried to reassure you has the right attitude. If s/he can do it so can you. Chill and carry on doing your job as conscientiously as you can.

Getting someones name wrong? Hardly an offence is it?
Without details can’t really help, but you need to stop beating yourself up about something so small, stand up straight and have confidence or you won’t be able to carry on in that role.
Put small knocks behind you and show others that all is fine with you.
Unfortunately women beat themselves up about minor problems when they really don’t need to.
If you do anything wrong or considered wrong at work, apologise and move on.