The general rule is: With singular nouns, do not use an article with proper nouns, that is, names. Otherwise you should use either an article, the word "one", or a possessive like "my" or "her". (I wouldn't swear that there are no other words that can take the place of an article, but those are the main ones.)
So normally, you would write, for example, "I am attaching an additional draft of the agreement." Note the "the" before "agreement". But you wouldn't write, "It was signed by the Fred Smith", just "by Fred Smith", because Fred Smith is a proper noun.
We often recognize proper nouns because they begin with a capital letter. But legal documents often capitalize words that have been given special meaning in the document. Like early on their will be a section of definitions, and it will say something like, "You means the policy holder." Then throughout the document they'll capitalize "You" to remind the reader of this special definition. This does not make the word a proper noun in a grammatical sense.
That said, the examples you give are not complete sentences, so it is meaningless to try to apply normal grammar rules. They sound more like titles or items from a bullet list. In such titles or labels, it's common to leave out words that are not necessary to make the meaning clear for brevity. For example, if someone writes an article about, say, a parade to be held on Thursday, they might give it a title of "Parade Thursday". This leaves out the article that belongs in front of "parade" and has no verb. Presumably it's sure for "There will be a parade on Thursday" or something like that.
That appears to be what is happening here. "Conclusion of additional agreements to Agreement for financial lease #12345" is short for something like, "We concluded additional agreements to the Agreement for the financial lease numbered #12345."