"Figure 1.1" isn't a noun followed by a proper noun. It's a noun phrase all of its own. You could say "on page 3, in the figure numbered 1.1", in which cased you use the definite article.
Your other examples aren't exactly what I would call a noun followed by a proper noun, but rather a noun followed by a label. I have no idea if that's a grammatical term, but it's like being on a game show and you're told to pick a door to win what's behind it and you choose, and they say "let's see what's behind door 3" if they're numbered, or "let's see what's behind door C" if they're lettered. In the number case, it would be normal to say "door number 3" as an alternative.
Hang on, this is going to be long-winded, because it's not simple.
"Use (the) function ABC" isn't so natural either way, because "ABC" is a name or title being used in a way that doesn't 'fit' normally - I was told that this is referred to as using it nominally, but I don't know if that's a normal usage of the term. You have the same situation when wanting to refer to a word rather than use the word as a word.
It's hard to explain how to tell when this applies; titles of books or films are almost always treated this way, and words in general are only treated this way if they are being used to refer to the word rather than to use it normally. For instance, when we are talking about how to use the word bulldoze, for example, it is being used nominally in a sentence like this. In an example sense, for example "they've come to bulldoze the house", the word is being used normally. When a word or phrase is used nominally, style guides generally recommend either italicising it (as I have done), or putting it in quotation marks. So, when writing about how to programme something you might say "call ABC()", and when saying it allowed you don't mention the parentheses. But when taking about the function itself, it might be quoted or italicised. A lot of style guides will recommend using teletype for function names, of course, whether using them nominally or not. So you would say "the function
ABC() is used to...".
In all three of your examples, whether or not you use an article, I would say that these are situations where you ought to mark the function, field or screen names with italic, teletype or quotation marks, depending on the style expectations of your audience.
Now, as to whether you need the article. Well, for normal everyday Standard English, whether formal or informal, you need the article. "Figure 1.1" is a fully specified name all on its own, by convention if nothing else, but "function ABC" is not, nor is "field Name" or "screen Transaction Data". Thus, I would expect something like:
Use the function
Fill in the field Name.
The button is present in the screen
(Also, on the last one, it might be more appropriate to use "on the screen", though that might depend on context.)
However, there are domain-specific language conventions to deal with, so there may be instances where it is more expected that you not use the article.