How to swap SetDelayed expressions?

Can't you just define a single function?

d[x_,y_]:=RandomVariate[UniformDistribution[{x, y}]];

Then call it as:

D1 = d[-1,0]

or

D2 = d[0,1]

There are different usages of SetDelayed. Read SetDelayed documentation, Section Scope > Diffrent Kinds of Values for more information.

This solution works on var := def (like your case) not var[] := def or other kinds.

Code

ClearAll[swapSetDelays];

SetAttributes[swapSetDelays, HoldAll];

swapSetDelays[a_, b_] := With[{temp = OwnValues[a]},
  OwnValues[a] = OwnValues[b] /. HoldPattern[b] :> a;
  OwnValues[b] = temp /. HoldPattern[a] :> b;
  ]

Example

SeedRandom[1];

r1 := RandomInteger[{1, 10}];
r2 := RandomInteger[{11, 20}];

{r1, r2}
(* Out: {2,15} *)

swapSetDelays[r1, r2];

{r1, r2}
(* Out: {11, 8} *)

In the rather unlikely case of you actually wanting to swap two definitions, e.g.

D1 := RandomVariate[UniformDistribution[{-1, 0}]];
D2 := RandomVariate[UniformDistribution[{0, 1}]];

You can do so temporarily

Module[{D1 = D2, D2 = D1}, Print[{D1, D2}]]
{0.863742,-0.710931}

If you've already used these definitions e.g.

print := Print[{D1, D2}]
print
{-0.349444,0.720738}

and would like to interchange them temporarily, you can use

Block[{D1 = D2, D2 = D1}, print]
{0.123198,-0.592611}

Needless to say, if you interchange them permanently, there is risk of becoming confused about how many times you've done it!