noun
pouch, pocketbook, handbag, bag, clutch bag, clutch, receptacle, portemonnaie (French), moneybag, wallet, pocket, coin purse, billfold, reticule, money belt, sack, vanity case, vanity bag, halfpenny-purse, belt-purse, sporran, bursa, saccule, poche, pochette (both French).
hold the purse strings*
be in control of money, finance, manage a household, manage a business; see manage 1.
tighten the purse strings*