Can anyone suggest a "name" for this progression
It's not an "officially named" progression (like "rhythm changes" or "backdoor cadence"). Without being unduly flip, I say just name it after yourself. It's now The Howe Progression.
Possible modes or scales that would work
One way to go about this is to look at the set of notes comprising the entire collection of chords, and see if they make a useful scale. Failing that, look at subsets of the progression to find scales that work. For more on this, see Finding a Scale from Power Chords.
In this case the chord progression uses every pitch except F, so breaking things up will better suit the purpose. Note that each pair of chords has common tones: C#m7 and A share C# and E; D#M7 and F# share A#; E and G# share G#. Another observation is that D#M7 shares no pitches with the preceding two chords, and E shares no common tones with either of its two preceding chords. This naturally divides the chords into pairs, and also suggests key changes.
- For the C#m7 / A pair, any scale containing up to four sharps will contain the chord tones (as would any mode based on that scale).
- The D#M7 / F# pair don't lend themselves to a single diatonic scale/mode, but I'm partial to an "invented" scale that can work with both:
C# D D# - F F# G - G# A A#. (The hyphens indicate the groupings I hear within the scale.)
- For the E / G# pair, I like C# Dorian over the E and I like the seventh mode of the C# melodic minor ascending scale. These two scales differ only by one pitch.
C# Dorian: C# D# E F# G# A# B C#
C# mel. min. mode 7: B# C# D# E F# G# A# B#
is E major a "correct" tonic chord for this musical passage?
IMO, no. I would put the progression in C# minor. This is because of the very strong pull of the final two chords. III-V-i is a reasonably "ordinary" progression, and the V-i relationship is especially strong. The reason III-V works so well is the combination of the common-tone (the G# in this case) plus the chromatic "leading-tone" movement: in this case from B to B#, with the B# leading to a presumed C#.