Will the logo of my game engine at the beginning of the splash screen improve the brand of my game/software? Will it have any influence on users that the game/software's graphics were created from the scratch by the developer? I know some of them really don't care how it was made and it's not their thing but will it somehow embellish my game? From my own perspective, I enjoy more playing games which have their own game engine, because they feel more dynamic and controlled, I just like them. Whats your opinion?

Just to note. I know it's impractical to create a game engine just to create a game, but my goal was to learn OpenGL because I was very interested and I feel more comfortable of possessing my own API rather than using a third-party engine, I feel more control over my app.

A splash screen can help to establish your brand, yes.

However, people won't necessarily assume you haven't used a third-party engine or assets just because you've shown a splash screen.

2 hours ago, Cofyka said:

Will the logo of my game engine at the beginning of the splash screen improve the brand of my game/software?

The whole concept around branding is to be unique. Using your logo at the start is exactly what everyone else does and can actually be harmful if your trying to make a brand.

Do something that sets you apart from your competitors. Lionhead Studios for example used there Logo as a Easter egg, in all there games you can find it hidden somewhere and in some like Black And White the logo was a mini game.

EA is known for using catchy phrases, I bet you can hear them just by me mentioning EA.

One thing you could consider is using a similar looking Start Menu for all your games; people quickly notice if the start menu is the same.

You could show the Logo only when the player starts a new game or after the tutorial; establish some kind of pattern that is unique, and your brand will form around it.

If you share some details we could help more with your brand. You can also consult a graphics designer; this is what they do and there are millions of them.

4 hours ago, Cofyka said:

Will the logo of my game engine at the beginning of the splash screen improve the brand of my game/software?

It won't improve it -- it marks and establishes your brand.