In my case for this moment I do as I make remixes of specific songs and most of the time I remix them in full. Not always but since I started making those remixes this is the approach I've taken. So yes, I include the title of the original and the name of the artist who made that particular song.
However, I'm thinking of a slightly different approach where I mix several different artists together. For example I make a drill beat and on that drill beat I put acapellas from three different rappers and I create kinda like a new song. From what I've seen this kind of approach helps getting more views as in this way you're targeting fans of three/four/five artists and people in general are interested in this kind of stuff (at least based on my observations). You can also "trick" people and add for example "Unreleased Song" to the title to create a typical clickbait title. But this approach takes more time as you not only have to take care of music but more importantly the lyrics and mix those lyrics so that they make some sense together.
I have no idea what's the impact on the algorithm when you put the name of the artist and when you don't. I kinda don't understand the question here, because if you create a remix, it's rather obvious that you made a remix of some song by some other artist.

Besides the algorithm doesn't look for the title but the content. So if something's detected it's rather based on things that were detected within your content (look for example at the videos where people curse - they get demonetized for using a bad language most of the time despite the fact no one put any bad words in titles). So for example if you made a remix of let's say Billie Jean by Michael Jackson and titled it like this:
Iron Keys - The Kid Is Not My Son
Then everyone would see some track by some unknown guy Iron Keys but the algorithm will most likely detect that you used Michael Jackson's work. So it kinda doesn't make sense to do it like that. It's less obvious for people. You will get completely different result if you write:
Billie Jean (Remix By Iron Keys)
First of all, you straight away inform people that it's Billie Jean ( a song that most people like and know), secondly, that it's a remix, and thirdly that it's made by you. The fact that it's made by you is actually the least important because personally I treat those remixes as an opportunity to boost my name on someone else's name. And I think everyone who ever made a remix thought about remixes in the same way.
Also what I noticed is the fact that you should play by YouTube rules. What I mean by this is simply following a typical YouTube naming convention. Take a look at what shows up in your main card on YouTube. If you take similar approach to music you can for example do it like this:
BILLIE JEAN BUT IT'S EDM
or
you won't believe what billie jean in trap version sounds like!
or
billie jean in trap version is pure madness!!!
I know that it's probably not the perfect naming convention for "artists" as we all dream of thousands of people who will be eager to click on a video titled like this:
Iron Keys - New Song
But it is what it is. You have to respect the rules of the platform where you post your music and just do it as the algorithm expects you to do.
However, at the same time these are just my observations. I try to incorporate some of the conclusions I was able to draw on my own channel but it's still a trial and error for me. Also you can't really predict what will be picked by algorithm and what won't.