What is the term for combining functions $f_1,f_2,\dots,f_n$ into a tuple $(f_1,\dots,f_n)$? This is an embarrassingly simple question, but I was not able to find a definitive answer from literature search.
Suppose one has some collection of functions $f_1: X \to Y_1, \dots, f_n: X \to Y_n$ on a common domain $X$.  Then one can form the function $(f_1,\dots,f_n): X \to Y_1 \times \dots \times Y_n$ in the usual fashion:
$$ (f_1,\dots,f_n)(x) := (f_1(x),\dots,f_n(x)).$$
My question is: what does one call the function $(f_1,\dots,f_n)$?  I had (without thinking much about it) used to call it the "direct sum" of $f_1,\dots,f_n$, before realising that this actually had no relation with the usual meaning of direct sum.  In category theory, one might call $(f_1,\dots,f_n)$ the "product" of $f_1,\dots,f_n$, but this could get confusing if $f_1,\dots,f_n$ already take values in some ring, so that there is also a pointwise product.  Is there some other commonly accepted term for describing the function $(f_1,\dots,f_n)$?  It doesn't sound quite right grammatically to refer to it as the "tuple" of $f_1,\dots,f_n$, and "concatenation" or "join" don't quite seem to fit either.
 A: You could call
$$\mathbf r(t)=\langle x(t), y(t), z(t)\rangle$$
the vector function (or vector?) of $(x,y,z)$.
A: Perhaps you can take inspiration from computer science.
In "APL: an interactive approach", Gilman and Rose talk about the catenation and lamination operators for joining together appropriately shaped arguments which (in my view) are multidimensional arrays.  I think 'catenating' functions is appropriate for this usage. (Gilman, Leonard, and Allen J. Rose. APL: an interactive approach. Krieger Publishing Co., Inc., 1992.  I have the second edition from an earlier year at home, with catenation on page 138, I think.)
If you decide that you prefer something else, be bold and define a term.  Although I like Brendan McKay's suggestion of 'assemblage', for some reason 'amalgam' appeals to me.  However, it is important to know how you end up using the name and the construct: there may be other things that better deserve those names.  Further, be sure to point out similar but different uses (e.g. 'amalgamated product'). (You know that already, but a reminder shouldn't hurt.)  You might even give a nod to history and note how such things were named and used in early vector calculus and linear algebra texts.
Gerhard "Can Say You Were Ill-advised" Paseman, 2015.10.06
A: I was encouraged to make my comment an answer: 
In the case $n = 2$, I would call it the pairing. Similarly, one has "tripling", "quadrupling", and so in general one might call it the ($n$-)tupling of the list $f_1, \ldots, f_n$. And indeed that is what the nLab calls it: see here. 
Whatever this should be called, I would not call it the cartesian product of $f_1, \ldots, f_n$. The product is a functor $\mathcal{C}^n \to \mathcal{C}$ whose value at a morphism $(f_1: X \to Y_1, \ldots, f_n: X \to Y_n)$ of $\mathcal{C}^n$ is rather the morphism $f_1 \times \ldots \times f_n: X \times \ldots \times X \to Y_1 \times \ldots \times Y_n$ of $\mathcal{C}$, and it's the latter that I would call the product of $f_1, \ldots, f_n$. 
I will see if I can track down further citations for $n$-tupling. 
A: A reasonable case could be made for calling your tuple-function a multi-span in whichever category $C$ your $\{f_i\}_1^n$ inhabit. When $n=2$, this reduces to the usual span given by roof-diagrams which look like this:
$$Y_1 \stackrel{f_1}{\gets} X \stackrel{f_2}{\to} Y_2$$ 
In this happy $n=2$ case you can actually compose these guys provided $C$ admits pullbacks; in this case, you have a bicategory of spans in $C$. For larger $n$, things are much less structured (as far as I know).
The obvious dual gadgets (unfortunately, but not unexpectedly, called multi-cospans) have actually appeared in work by Grandis, pdf here.
