earth - From what distance can one object influence gravity of another object?

What id like to know, in what distance do they have to be from each other to create only one gravitational influence.

At whichever point you decide to call them two objects rather than one object. It's a completely arbitrary choice that depends on you rather than gravitational physics. What's going on is that gravity can be described by a mass density distribution, and which part of that distribution corresponds to "one object" and which to "another object" isn't important.

You may be confused by Newton's law of gravity that says the gravitational force force is proportional to the product of the masses and inversely proportional to the distance between them squared. But this law only applies to spherically symmetric objects. It only applies to you exactly if you're a spherical cow.

This kind of arbitrariness actually applies to the Earth as well. Even if the Earth were perfectly spherically symmetric, one could say that Earth's gravity is due to the influence of the northern hemisphere and the influence of the southern hemisphere, etc. Whether you consider the Earth to be one object, or two, or a trillion, depends on you.

The Earth isn't spherically symmetric. It's closer to an oblate spheroid, since it bulges at the equator. But it isn't exactly that either, having mountains or other topographical feature, to say nothing of mass density variations inside the Earth. In principle, one could describe its gravity including people and trees or whatnot. Gravitationally, there is no fundamental difference between you and some rock. That you consider yourself to not be "part of Earth" is a choice you make for other reasons.

If you distance yourself from the Earth, there is a difference because the mass distribution would change. But again, whether you consider this to be "only one gravitational influence" or "the Earth plus you" is up to you, and this holds true regardless of whether you distanced yourself or not.