Is $E[XX^T]$ also called a product moment? I've found a related question which was for product moment $E[XY]$. Is $E[XX^T]$ also called product moment or is there a special case name for it? This is the first term of the covariance matrix $Cov(X) = E[XX^T] - E[X]E[X]^T$.

I don't know if there exists a special name for $E(XX^\top)$ but since
\begin{align}
XX^\top=\begin{pmatrix} X_1 \\ \vdots \\X_n\end{pmatrix}\cdot \begin{pmatrix} X_1 & \dots & X_n\end{pmatrix}=\begin{pmatrix} X_1^2 & \dots & X_1X_n \\ \vdots & \ddots & \vdots \\ X_nX_1 & \dots & X_n^2 \end{pmatrix}
\end{align}
you get:
$$
E(XX^\top)=
\begin{pmatrix} E(X_1^2) & \dots & E(X_1X_n) \\ \vdots & \ddots & \vdots \\ E(X_nX_1) & \dots & E(X_n^2) \end{pmatrix}
$$
Therefore, I think that it is valid to call this matrix the matrix of product moments, or product moment in a multivariate setting.
