The Real Madrid home jersey came with LFP or La Liga badges pre-stamped prior to the 2017/18 season.
The inaugural 2017/18 season so a La Liga nameset being mandatory for all teams competing in the two top-flights in Spain.
Thus the pre-printed sleeve badge was scrapped because it would not necessarily fit with the style of name and number printing on the jersey.
But the season 2016/17 would still see a stitched pre-printed La Liga badge to the right arm sleeve as default, standard.
Here is the La Liga logo. It is stitched and replica size, 8 cm. Strange why adidas would not apply player’s size 10 cm and in plastic since that is what the players would wear on the pitch.
For many seasons Real Madrid would not have a sleeve badge to the left arm sleeve. Only by the season 2023/24 was a sleeve badge introduced. HP became the sleeve sponsor.
The official name and number kit was provided by the company Sporting ID. Only for the 2020/21 season did Avery Dennison take over the license for the official RM printing.