Is it bad luck to change a horse's name? People will often tell you that. I don't think so, but I think it's nice if a horse's name can stay with him, so it doesn't seem like he's trying to join a Witness Protection program.
Can't say I like the name 'Mena'. Too close to 'Mean' and a lot of snickers and teasing.
Can't say I mind the name 'Philomena' either. A nice name for a classy gal. Conveys dignity and strength to me, it is a Greek name that means 'Strong Friend'. Philly is a nice stable name to go with it. Some people may not like the name because they are not familiar with it.
I think YOU need to name her something that means something to YOU. Surely something happened that she does or happened when you bought her that means something special to you.
If she tends to always be playing with her stall ball, for example, with stable name in parentheses, you could call her Anna K ('annie') or Martina N ('marty') after the famous tennis players. If she's always cool and calm, you might call her 'Queen Jane' ('janie'). If she's got a chip on her shoulder, name her after a famous warrior, like 'Boudicea' ('Bo') or bandits 'Belle Star' ('bell' or 'star') or 'Foolan Devi' ('devi').
I tend to shy away from names like 'Sassy' and 'Babe' and common names like it, for a show name. If only because your entry is likely to get mixed up with another.
Horses tend to get a show name that sounds unique and has something to do with the person or how the horse came to be with them or the type of showing they do.
That doesn't have to be the same as their registered name. The registered name usually is some combination of their ancestor's names.
It's not unusual for a horse to have 3 names - show name, registered name and stable name.
Each type of showing/riding tends to have typical names for a horse.
Dressage horse names are tending toward one word, usually something very dignified or unique. Authors, artists, names of wines, opera characters, things like that.
Reining horse names were traditionally very 'cowboy'ish. Or related to their ability to win, like 'Line My Wallet' or 'Cash in the Bank', jumper names tend to be 'winning' names t too.
You're in hunters? Many names for hunters tend to be kind of plays on words or clever sounding phrases, or local names. Some of them are a little sappy to my ears, or a little too cute cute cute, but that's what is used in that division. 'Don't Tell Daddy', 'Mark of Excellence', 'Totally Natural', 'Inside Scoop', 'Consider Me Lucky'. Not recommending, just saying those are typical show hunter names.