This is a pretty loaded question since there are 1000s of different design styles + people with different personalities, but here is what I think is the most efficient way to go about this.
Portfolio logos are generally reflective upon your brand(you working) and I like to throw my personality in to it as well. You have to decide what you want the receiver (prospective) employer to feel. Do you want them to remember you for your design, typography, colors or even more personally, your face?
My advice is to go through a lot of literature on color/shape theory, find out what gives people what kind of thoughts. How to appear dynamic, while also staying clear, concise and clean. But ultimately, your logo should reflect you, not someone else's taste.
Grab a notebook, write down some adjectives about how you want to be portrayed, (ie: clean, cutting-edge, dynamic, modern & professional). Then start some thumbnails based on the words.
Just to give an example: Modern & clean would most likely have a lighter sans-serif font with some crisp lines in your illustration. The text might have a little more letter spacing and appear light weight.
As an added bonus, this is the process I used on my logos for V1 / V2
Some people enjoy using just Their Name | Graphic Design (or what ever field). That's cool, but i like to stand out. I'm a pretty weird kid, and about 2 years ago I first created my portfolio and I wanted it to show off my illustration and color theory. I was 19 at the time so being silly and weird was still pretty viable.
In the V1 of my portfolio, I literally used my face. I chose this because when I was graduating college, I genuinely wanted people to remember my face, and what better way is there than to plaster it on all my branding!
Then when the redesign came around, I was learning more and more and became more of a front end web designer, than I was a graphic designer. I wanted to reflect that, with low-poly being a large web design trend, I chose to go this route with a simple low-poly "T" which adds some depth to the letter, but also plays off my website's design.
