Meaning of name the day

[Veki]

Test No. incompl/inter-38 "Save the Day", question 7

After a very long engagement Mike and Mary decided at last to ......... the day.

(a) state
(b) mention
(c) name
(d) hold

Test No. incompl/inter-38 "Save the Day", answer 7

After a very long engagement Mike and Mary decided at last to name the day.

Correct answer: (c) name
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Does it mean they have to agree the first between them (because they still don't know the date) and after that they will inform their family and friends, OR they already know the date and "name the day" meaning they have to only inform family and friends?

Thank you a lot!

[Alan]

An expression often used in proposed marriages when the two people announce to everybody that they are getting married and also say when that will be.
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English as a Second Language
You can read my ESL story A day in the life of a stately home owner