[DaiPlusPlus]

I'd trim-off the "Junior" and leave it at that. For a formal job-title (as HR would demand) it's common to have Roman numerals appended, e.g. "SWE I" and "SWE II" before you get "Senior". The semantics is the same: "SWE I" == "Junior SWE" but without the unpleasant connotations that the term "Junior" specifically has, especially when you have older folks coming in at an entry-level (e.g. from coding-camps or a midlife career change) where referring to a 40something as "Junior" just feels weird.

That's how it's done at all the US software companies I've worked at, including Microsoft and some startups.

My current company does has done away with job-titles entirely and we make up whatever we want on our business-cards (within reason).