How to create this background with GIMP

[PixLab]

The fast way
Filters ➤ Render ➤ Noise ➤ Solid noise... adjust with sliders
Then
Colors ➤ Colorize... adjust with sliders and chose your colors in it
Or if you want a gradient (multiple colors)
Colors ➤ Map ➤ Gradient map select the gradient you want before using it (in the gradient tool)

Now to get almost exactly the same result as your image
Filters ➤ Render ➤ Noise ➤ Solid noise... Details ➤ 5
Then Filters ➤ Render ➤ Noise ➤ Plasma... Mode ➤ Addition
Then Colors ➤ Desaturate ➤ Desaturate... Select the mode you like the most
Then Colors ➤ Invert
Then Colors ➤ Colorize... Chose your color, then play with lightness and saturation sliders

Result (not changing the sliders, just the color)