In the BibTeX and biblatex tradition theses (@phthesis, @thesis, ...) don't have a publisher. Instead they have a institution or school. Most dissertations can probably be found without giving the publisher (if they are published by a known publishing house at all).
That all said, it is certainly not impossible to add a publisher to theses. You just need to find a good place to hook in to. The bibliography output of the ieee style is based on the standard biblatex style standard.bbx, where the institution of a @thesis is printed in institution+location+date. You can modify that macro to also print a publisher.
\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[style=ieee]{biblatex}
\renewbibmacro{institution+location+date}{%
\ifentrytype{thesis}
{\printlist{publisher}%
\setunit{\addcomma\space}}
{}%
\printlist{location}%
\iflistundef{institution}
{\setunit{\addcomma\space}}
{\setunit{\addcolon\space}}%
\printlist{institution}%
\setunit{\addcomma\space}%
\usebibmacro{date}%
\newunit}
\begin{filecontents}{\jobname.bib}
@phdthesis{phd,
author = {Me},
title = {My Title},
school = {My University},
year = 2020,
publisher = {Fubar},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
Lorem \cite{phd}
\printbibliography
\end{document}

note= "Fubar"instead ofpublisher= "Fubar"? Aside: Most Ph.D. dissertations don't have publishers. If yours is published in book form, you may want to consider switching from the@phdthesisentry type to the@bookentry type. – Mico Aug 10 '20 at 19:07