Then it is unfortunate that you entirely missed the point of my post.
There is no good answer to that as a general question, and it is going to depend on a lot of other factors. In the example you gave, it is going to depend heavily on your intent and what you end up doing with the domain name.
In the general case, it is also going to depend on what sort of trademark we are talking about. Not all trademarks are created equal. It's going to depend on whether it is inherently distinctive, arbitrary, suggestive or descriptive with acquired distinctiveness, along with the relative degree of fame.
I'm sorry you aren't interested in a more comprehensive discussion that would lead to a deeper understanding of some relevant principles of trademark law. One of the problems here is that you have this idea that one of the "correct" answers to your question is going to be among the multiple choices you propose above, and you seem upset at me for suggesting otherwise.
Here's a question - I found a plant growing in my yard, and I think I'd like to eat it. If I only eat the roots of the plant, instead of the leaves or the fruit, is that going to be the best part? Who knows? It's going to depend on the plant and how I cook it, don't you think? Is it a carrot or a tomato?
In your example, you left out the important part, and those are the questions I posed in response. Obviously, "Gun Lake" is a lake in Michigan - a geographic location. Now, in another thread, I wrote a comprehensive set of posts on geographically descriptive terms and their use as trademarks versus geographic descriptors:
https://www.namepros.com/threads/novi-a-city-in-michigan-trademark-application-by-facebook.1236817/
So, it's going to matter whether or not, for example, the domain name is on PPC and showing casino ads, or whether it is selling real estate between Grand Rapids and Kalamazoo. It depends on the circumstances motivating you to register the domain name and how you end up using it. That's the point. I'm sorry you didn't understand it, but if you don't like my posts, this forum has a convenient ignore feature.
But, golly, a whole thread about the name of a town in Michigan last week, and now one about the name of a lake in Michigan. The general point didn't change that fast.
That addresses a limited situation where the "part of the trademark" is itself a geographic term, but certainly isn't a general answer to the question.
But, hey, there's a ton of folks here at Namepros who have no idea what they are talking about, and will be happy to give you whatever answer you want to hear, rely on, and get into problems with.
I'm sending you a complete refund of every penny you paid.