[рони]

Tachyon,
вариант...

let str = `<tag1 name1="value1" name2 = 'value>>>>><<<2'>
 < tag1 name1="value1"name2 = 'value2<<>>>' >`;
let reg = /<\s*?\S+((['"])[^'"]*\2|[^>])*>/gi;
console.log(str.match(reg))