I saw some photos of medailist from japanese championships (from All Japan Judo Federation Facebook page) They used the Mizuno gold (with IJF approved label) type obi often and their obi contain some japanese kanji with their name (surname).
I saw the name of obi in Europen judokas too time to time (in latin characters).
It is caprice only or anything else?
I dont know how is it in judo exactly - in some Budo is anything similar... the carrying of name on own equipment is politeness and it makes easier be adress (connect, appeal) by sensei (japanese mainly), next is identifying during shiai
In modern ZNKR iaido iaidokas used nafuda (nameplate on the left side chest on their gi) during practice outside their home dojo.
In modern kendo kendokas used zeken (nameplate on the tare - part of kendo armor) - allways.
Some japanese manufacturers of judo equipment give some informations for name on the belt.
1 Embroidery fonts and print body only
1 Embroidery location / coat: (1) or (2) pants: ( or (9), select
* Embroidery at the 3, 4, 5 will be estimated separately.
1 Embroidered letters and 'last name', 'name', 'last name', and other (fill to the remarks field)
1 Embroidery thread color and black, red and gold tea (orange), gold, silver
It looks like that embroidered name on the obi is common in japanese judo... IJF judokas uses the backnumbers in this time, the name on obi could be just the little bit traditional way.
Thank you for your explanation about it, if you have some own experiences.