What's the usual name for a 'dot' billboard?

This is known as a variable message sign, or a matrix sign.

A variable- (also changeable-, electronic-, or dynamic-) message sign, often abbreviated VMS, CMS, or DMS, and in the UK known as a matrix sign, is an electronic traffic sign often used on roadways to give travelers information about special events. Such signs warn of traffic congestion, accidents, incidents, roadwork zones, or speed limits on a specific highway segment.

According to Ngram, "matrix sign" is slightly more common.

Here's a picture, from Wikipedia:

I would call it an LED matrix, an LED sign, or an LED billboard.

From a quick search on Google Images I find that the term LED matrix seems to be mostly used for smaller scale devices which you could keep in your pocket.

Calling it an LED sign or an LED billboard would indicate that you are talking about something larger. A Google Images search for either of those terms will mostly find more modern technology with RGB and higher resolution.

If you specifically want to talk about the kind with only one colour as in your picture, the term to use is monochrome as in monochrome LED sign or monochrome LED billboard.