Preferably as specific a term as possible (i.e. not applying to other phonological rules).
For example how English words can't begin with "ng" or how Spanish words can't begin with "st"
The term you're looking for is phonotactics. From Wikipedia:
Phonotactics (from Ancient Greek phōnḗ "voice, sound" and taktikós "having to do with arranging") is a branch of phonology that deals with restrictions in a language on the permissible combinations of phonemes. Phonotactics defines permissible syllable structure, consonant clusters, and vowel sequences by means of phonotactical constraints.
"Admissibility", according to Halle in "Phonology in Generative Grammar". Stampe has also used this term to refer to a theory of what words are permitted in the lexicon of a language with a given phonological system. Halle's early theory was that forms are lexically admissible when their addition keeps the grammar as simple as possible by not forcing the repeal of any lexical redundancy rules.
In SPE, there is proposed a way to measure distance from the lexicon of a potential new lexical entry by counting the symbols in the phonological rules that would be required to change the new entry into some preexisting lexical form. (I don't think this makes sense, because then the admissible forms, at distance zero, would be only those forms already in the lexicon.)
In Stampe's natural phonology, the admissible forms are those to which no process which could apply to an underlying form is applicable, and foreign words are made admissible during borrowing by applying such applicable processes. Processes which are prevented from applying directly to underlying forms by ordering constraints do not affect admissibility.
The term "phonotactics" comes from older taxonomic phonemics, and is generally used to refer to an enumeration of facts about the phonemic forms allowed in a language, without involving anything about the rest of the phonological system or how borrowing new forms into a language works. Generative phonology and Natural Phonology are in agreement that although linguists can invent "phonotactic rules", of course, there are no such rules in phonological systems.