Grammatical name of the form used before -て, -たり, -た, -たら?

Question

I'm looking for the Japanese name of the specific verbal form used before -て, -たり, -た, -たら:

verb      → 連用形 ren.yōkei → XXXX    →   + -て, -たり, -た, -たら
書く      → 書き             →  書い   →   書いて, 書いたり, 書いた, 書いたら

I assume this verbal form is derived from the 連用形{れんようけい}, with specific phonetic modifications for godan verbs. (see Shimamori Reiko, Grammaire japonaise systématique.1.48 (my translation): "-て, -たり, -た, -たら are preceded by the connective base of the verb, [...] yodan verbs [...] being deeply modified [by the suffix]")

So, what's the name standing for "XXXX"? Something like "-t" form?

Answer 1

They are also treated as 連用形. More specifically i-type are called 連用形のイ音便. Sometimes 音便形 is used, but there are no official name.

References

1. 音便形 in デジタル大辞泉
2. 動詞の音便（おんびん） イ音便・撥音便（はつおんびん）・促音便（そくおんびん）
3. 音便 - Wikipedia (Note: This article uses 動詞のテ・タ形 for conveniece sake.)

Answer 2

The way I like to explain euphonic changes (音便) is by modeling it in terms of "repairs":

　/kakite/
　　⇓　　{devoice of /i/}
× /ka[kt]{LL}e/
　　⇓　　{/k/+C sequence repaired to /i/+C}
　/kaite/

Namely, a vowel devoices, and then some sort of repair needs to happen due to what sounds like a consonant-consonant sequence (which are illegal). Depending on what consonants are involved, C₁C₂ repairs as follows:

• イ音便: C₁ ∈ {/k/} ⇒ /i/+C₂
• イ音便: C₁ ∈ {/g/} ⇒ /i/+voiced C₂
• 撥音便: C₁ ∈ {/m/, /b/, /n/} ⇒ /N/+voiced C₂
• 促音便: C₁ ∈ {/w/, /t/, /h/, /r/} ⇒ /Q/+C₂.

The only exception to these rules I'm aware of is 行く, which unexpectedly turns into 行って (i.e., following 促音便) instead of 行いて. It's probably just due to イイテ being weird to pronounce. I also discuss this in this answer.

I don't think there is a real point in giving a name to the repaired stem alone, since it does not actually exist outside of the appropriate context.