I’m sure this type of join has an official name, however I don’t know it! I find it very useful for joining two slippy yarns when I’m working in the round. Do be aware that it creates several stitches on each side of the join that are thicker. For fine to medium weight yarn this isn’t noticeable, however as yarn becomes thicker it makes a less attractive join.
Work to within a few inches of the end of your working yarn. If you are working in the round you may wish to cut the yarn so that the join is around the side seams rather than in the center of the front or back.
Loop the end of one yarn with the start of the new yarn. I’m using two different colours to make the join more obvious.
Knit the last few stitches with the end of one yarn, holding the two layers of yarn double.
Knit the first few stitches with the start of the new yarn, holding the two layers double.
When you are finished you will have two tails left, I like to weave these in for a few stitches before cutting. Here is how the work looks after the new yarn is joined: