Naming half the fleet "...Tigress" is not going to work out well. Assuming they actually, do verbal communications its a mess.
Ruling out all but one of each tiger, lion, leopard, etc. would be a PitA, so I'm assuming that ultra-tech signal technology is up to the challenge.
Also, there are many nationalities on Earth and in 3I that have pouncers beyond those listed. Looking for different languages is one approach.
Didn't I include one or two of those? Anyway, going that way makes things too easy. Just by going with Danish I could practically triple the pool of potential names (Danish has two ways to create a feminine form, the prefix 'hun-' and the suffix '-inde'. So
Huntiger, Tigerinde, Hunløve, Løvinde, etc.. I very much doubt I'll be expanding the list to the full 200, but if I do, I'll probably use some foreign language names.
And it's not just any pouncers. It's Terran great cats, Terran great cats transplanted to other worlds, and alien pouncers named after Terran great cats. Genus
Panthera and its copycats
1, so to speak.
1 Pun intended. 
What message is this sending to the Aslan? Our best ship is named for their genetic peer. Do they call their ships, "apes"?
That's not down to me, is it? The
Tigress class is canonical. But if you ask me, it tells the Aslans that the Emperor doesn't lie awake at night thinking about how important it is to placate the Aslans.
The first 3 ships are the named ships in Canon. Coincidence?
No coincidence at all. Tiger, lion, and panther are three names that springs readily to mind when thinking about great cats. Which is presumably why the original writers came up with those names for the three ships they named. I assumed that they would likewise spring to the mind of the big brains at the [Imperial Naval Office for Coming up with Ship Names].
(It's three of the first four ships, BTW.. I put
Leopardess before
Pantheress, precisely to lessen the match a mite.)
And while I would include the
Lioness and the
Pantheress in the list of the eight
Tigresses stationed in the Spinward Marches (because canon says they are), I don't think I'd include any other of the first eight built. Unless some Traveller writer has the lack of originality to name another Spinward Marches
Tigress, Leopardess.
Also, I agree with statements that it's not the best dreadnaught design?
If someone sits down and designs a
Tigress that works I'll be the first to applaud, but it's really not what I'm concerned about here.
I certainly appreciate the display of good will. Our arguments have not made me angry with you and I'm pleased to see that they haven't made you angry with me. Thank you.
Hans