I am, Yours, etc

[kadioguy]

etc
abbreviation

et cetera — sometimes used especially formerly to shorten a letter-closing formula

I am, Yours, etc

(from Merriam-Webster Unabridged Dictionary)
--------
I found the following about 'Letter Closing Examples', but I still don't know what 'I am, Yours, etc' means.

How to End a Letter (With Closing Examples)
https://www.thebalance.com/how-to-end-a-letter-2062308

 

[GoesStation]

Long ago it was customary to end letters with long phrases like I am, and shall ever remain, your obedient servant, FUDDLES.

People on friendly terms would shorten such tedious messages to things like I am, etc., FUDDLES.

You will never need to know this unless you read old letters or literature containing them.

 

[kadioguy]

Long ago it was customary to end letters with long phrases like I am, and shall ever remain, your obedient servant, FUDDLES.

Is this servant's name FUDDLES?

 

[bubbha]

The person writing the letter is not actually a servant. The person may be a subordinate, or even an equal, but is just using self-deprecating language in the interests of etiquette. It's similar to the use of 敝 for oneself vs. 貴 for the letter recipient in Chinese.

But in this case, the letter writer's name would be Fuddles.

 

[kadioguy]

But in this case, the letter writer's name would be Fuddles.

Why not But in this case, the letter writer's name will be Fuddles?
Is your sentence a implied conditional?

Do you mean But in this case, the letter writer's name would be Fuddles (if I knew the answer)​?

Does 'would' here mean 'used for saying or asking what someone thinks about a possible situation', whereas 'will' mean 'used for showing that you are fairly certain that something is true'?
-------
(update)
I think no one will reply, so I am posting a new thread here.