The is used to signal that we are talking about a specific noun mentioned previously conversation/context, or observable by those in the conversation. A/an X is used to signal that we mean any of X and not a specific X mentioned earlier.
Some nouns are considered "observable" by others by default, especially if the noun is a big thing that affects/impacts everyone, or is considered well known by everyone. Examples include the sky, the ground, etc.
Context can control what is "considered well known by everyone." In this case, your sentence is talking about a C library and I'm assuming part of the target audience for your text are likely programmers.
So, regarding "C++ class library named LIBNAME":
Is this a well-known standard library that any C programmer should have heard of? Such as
<stdio>? Use the in that case. If you are addressing non-programmers though, they may think they have missed something, or feel left out.
Should the reader have heard of this library before, perhaps in earlier chapters or earlier volumes of the text? Then, use the.
If this is not a well-known library by your target audience, and you introducing to the reader to it, then it cannot be "mentioned previously" or "observable" and you should use a to talk about it the first time. Afterward, you use the to talk about it.
This assumes this is the first sentence that mentions LIBNAME.
Now, is your book titled "LIBNAME"? Do you have a chapter title visible above this text that says "All About LIBNAME" or similar? Some writers might consider that as "previously mentioned," and would use the based on that. That's OK too.