Because it is a Tensor. People do not deliberate much on choosing letters, as one can see from Gauss's $E,F,G$, among other examples. It happened to be the first tensor that came up in Sommerfeld's On the Theory of Relativity I: Four-dimensional Vector Algebra, p. 767ff, after he dealt with 4 and 6 vectors and then scalar and vector products. It was the turn of Tensor product. Minkowski and Abraham before that used different letters. Von Laue after followed Sommerfeld in his 1911 textbook on relativity (the very first one), and so it stuck, see History of Topics in Special Relativity/Stress-energy tensor.

Btw, $T_{\mu\nu}$ is typically just "stress-energy tensor", despite the momentum components in it. The stress–energy–momentum pseudotensor is a modification by Landau and Lifshitz, typically denoted $t^{\mu\nu}_{LL}$.

Because it is a $T$ensor. People do not deliberate much on choosing letters, as one can see from Gauss's $E,F,G$, among other examples. $T$ happened to be the first tensor that came up in Sommerfeld's On the Theory of Relativity I: Four-dimensional Vector Algebra, p. 767ff, after he dealt with $4$- and $6$-vectors and then scalar and vector products. It was the turn of $T$ensor product. Minkowski and Abraham before that used different letters. Von Laue after followed Sommerfeld in his 1911 textbook on relativity (the very first one), and so it stuck, see History of Topics in Special Relativity/Stress-energy tensor.

Btw, $T_{\mu\nu}$ is typically just "stress-energy tensor", despite the momentum components in it. The stress–energy–momentum pseudotensor is a modification by Landau and Lifshitz, typically denoted $t^{\mu\nu}_{LL}$.