Why are some random physical quantitites given a name?

[Kumar8434]

$\frac{dp}{dt}$ is given the name 'force' but $\frac{dp}{ds}$ has no name. I know 'force' is useful for calculations and predicting the future of the system. If 'convenience in calculations' is the reason why some quantities are given names, then I don't see why $\frac{dp}{ds}$ doesn't have a name.
Let's call $\frac{dp}{ds}$ 'x-force' denoted by $x$. Then if x-force is a function of time $x(t)$, then,
$$\int_{t_1}^{t_2}x(t)dt=m(\ln(v_2)-\ln(v_1))$$
which looks similar to the work-energy equation:
$$\int_{s_1}^{s_2}F(s)ds=\frac{1}{2}m(v_2^2-v_1^2)$$
So, x-force can also be used for calculations but is not given a name. Then, what is the basis for calling a physical quantity important and giving it a name?

 

[A.T.]

Let's call dp/ds 'x-force'...

Yeah, call it what you want, and then go on to stuff that actually matters.

 

[Kumar8434]

Yeah, call it what you want, and then go on to stuff that actually matters.

If you don't like the name, then maybe use $force'$. But why doesn't it matter? I've shown that we can also do calculations with it and predict the future of a system.

 

[A.T.]

But why doesn't it matter?

If it matters to you, name it what you want and be happy.

 

[Drakkith]

There's no simple answer to your question, but I'd bet some factors include how often these quantities are used, their relationship to other quantities, whether they can be derived from other quantities or not, along with other factors. Some quantities have names but are rarely used. For example, the 2nd derivative of acceleration is known as jounce, but you probably won't encounter that term very often.