There are some names that would work for Dutch,French,Italian etc but not quite so well for English example ''tense(focused)/lax(looser)'',''acute(at an angle)/grave(being pulled down from gravity)'' and ''checked/free''.If you want a quick Linguistic answer then go to the very bottom marked with an *.
The matter is (and you might know already) in many languages long and short vowels are not the same exact sound but longer,even though not as extreme as English they still differ for each other example in Standard-Netherland-Dutch(even though in some other accents they are the same)
long e is[e] short e is[ɛ]
long a is[a] short a is[ɑ]
long i is[i] short i is[ɪ]
long o is[o] short o is[ɔ]
long u is[y] short u is[ʏ]/[ə]
long oe is[u] short oe is [ʊ]
In English almost though out its history the long and short vowels where nearly always different from each other resembling modern dutch's at their closest(there might have been some accents that had short vowels and long vowels being the same phoneme but longer and shorter versions however they seem to have been less common since more precision is needed and people are generally sloppy)
The problem with ''tense/acute vs lax/grave''is that with e,a,u and o the names work fine
tense e is[i] lax e is [ɛ]
tense a is[e] lax a is [æ]/[a]
tense o is[u] lax o is [ʊ]
tense o is[o] lax o is [a]/[ɑ]
tense u is[ʏ̯ʉ] lax u is [ʏ]/[ə]
but not with ''i'' where it breaks the rule by having the long now renamed tense[aɪ] laxer than the lax [ɪ]
so you bothered with a new method to clarify but still have unclear zones.
Then there is ''checked'' and ''free'' vowels this one might be a better name,checked vowels are all the vowels that have to have a full consonant behind(w and y are semi-vowels) to be said in this way,as:
while free vowels can be anywhere including the end,as:
[e],[i],[aɪ̯],[aʊ̯],[o],[u],[ʏ̯ʉ],[y] (hay,glee,bye cow,no,roux,you,ew)
this system however also has a tiny problem and that is short u now renamed checked u [ə] is really a free vowel eg:cup[kəpʰ] vs america[ə'mɚ'ɪkə] also this method would not work with dialects where r is silent and r is not replaced with [ə] after the previous vowel for example ''beer'' becomes [bɪː] rather than [biɚ]/[biə] along with a long list eg: [bɛː]bear and [hɜː]her or even [lɛː]layer and [lɔːɪː]lawyer further more there is the exception in spa [spɑː]/[spaː], bra[brɑː]/[braː],even though minor kinds you are still not creating a system that is less complicated than the one there is.
Long story short (pun kinda intended) ''Long'' and ''short'' work better even though not literally meaning the vowel is the longer or shorter version of the same/similar sound, it's a way of saying/and idiom/alternate meaning in context ,the same way that a slim-chance and fat-chance mean the same thing and wise-man and wise-guy are opposites or in dutch I love you is ''Ik hou van u'' literally ''i hold from you'' and in french ''clair de lune'' literally ''clear of moon'' is moonlight.
*Given length or not in linguistics:
''i,y,e,ø,o,ʉ,ɨ,u,a,ɘ,ɵ,ɤ,a,ɶ''(some disagree on ''a''and ''ɶ'') are ''tense''
''ɪ,ʏ,ɛ,œ,ɒ,ʊ̈,ɪ̈,ʊ,æ,ɑ,ɔ,ɛ,ɐ,ʌ'' are ''lax''
''ə'' is ''neutral position''
ɑʊ̯/aɪ̯/oʊ̯/eɪ̯/øʏ̯/oʏ̯/oɪ̯ə/aʊ̯ə/ɪ̯ɛə̯ːoʊ̯ etc. ,any two(or more) vowels sound put next to each other are diphthongs/triphthongs and so on,when a vowel sound rises to a higher vowel sound it's a rising diphthong eg:[eɪ̯]''a'' while when a v.sound falls into an other lower vowel.s it's a falling diphthongs eg: [ɪ̯ɛ]''yeah'', combination diphthongs [aʊ̯ə]''Flour/flower''and same stress diphthongs [eo]''neo''