The only skill you really need
The only absolute must-have to be a service designer is less a skill than a mindset: curiosity.
The skills that make a difference
But over the years, I've noticed that there are a few skills that give me a bit of an advantage in comparison to other service designers or consultants:
Graphic Design
Being able to create a prototype visually by yourself or create a nice-looking presentation is certainly a skillset that I recommend you acquire as a service designer.
Understanding of coding
You don't know to be a great coder, but understanding how coding works and how computers work helps whenever you have to design digital services. And many services today have at least one digital element.
Ease with words
That's something where I'd love to get better. I have no problems finding words to express myself, but contrary to other people, grammar and syntax is a big issue for me. A lot of the service design job is in translating ideas and findings into clear words, and if these words come quickly to you and aren't full of mistakes, it's a big plus.
Project management
That's a skill I had to learn, but being a service designer often has a lot of project management that comes with it.
Surely, you can't learn all of this in one go.
What skills do I recommend you learn first?
Now, with more distance, I recommend that people learn these skills in that order:
project management first
graphic design,
ease with words,
and understanding of coding.
Why? Because if you can manage projects well, you can get help for the rest easily, and once you can express ideas visually and manage projects, you're already at a very good level.