For general portraiture, with a DSLR or mirrorless camera, a range of focal lengths between 50mm and 105mm is quite workable. Of course with various sensor sizes there is going to be differences in FIELD ANGLE but there are other factors to consider.
A "portrait" can be a tight headshot, a traditional head and shoulder image, a 3/4 or full-length image or even a group of two or more subjects.
A moderately longer lens is preferred by most experienced portraitists to help in avoiding certain distortions and thereby maintaining proper perspective, however, perspective is not controlled by focal length but rather by distance. The "proper" focal length for the type of portraits you are making enables you to work at a comfortable distance whereby you can easily communicate with your subject and maintain good perspective, both elements at the same time.
Somewhat longer lenses can make background management and selective focus easier to achieve. It can be less difficult to put a background out of focus sufficiently to obtain better "bokeh" and help subdue distracting background elements.
Perhaps a zoom lens that would encompass a range of theses prescribed focal lengths would be a good solution to your issue. You could vary the focal length according to enabling a practical and aesthetically pleasing working distances and make variations for the aforementioned types of portraits.
There are no currently manufactured lenses (for DSLRs) that are specifically designated as "portrait" lenses. Many years ago in the film era, there were lenses with that designation in that they were of the correct focal length, as explained above, for large format studio cameras and many were soft-focus formulas. There are some classic favorites for the 35mm format such as the Nikor 105mm- it is not a soft-focus model. Canon produced a 135mmm soft-focus model that ostensibly is a "portrait" lens. Nowadays, in digital photography, it is your choice depending as to the style you wish to produce, the type of work you are doing and the equipment you presently own. A portrait can bee tack sharp, sentimentally soft, or very soft- it depends on taste, style and approach. A lens does not need to be razor-sharp for every style of portraiture so even a so-called "kit" zoom may do very nicely.
The 85mm is not the "gold standard"- something in that range or the equivalent for your camera body will suffice.
Here on the UHH forum, there is an Advanced Portraiture section where you are welcome to participate- ask questions, get answers and critiques, join in the discussions and pick up some of the finer points.
PS- All this optical theory is great, however, a good rule of thumb for beginning to master portraiture is to put down the books on optics, the calculators and the computer keyboard and pick up the camera. Pop on a lens of one of theses suggested focal lenghts, recruit a willing subject who does no mind beig tortured and (just a little) at try you hand at it. Post some shots in the section I mentioned and get some pointers. Once you get your sea legs, then you can invest in you favorite lens.