Similar to the other responses, I you can still use a meaningful name, and just add your number to the end of it. Useful for debugging purposes:

lncount = 1
DO WHILE vwmactionnot.actionno = 1
        cNewAliasName = "membership" + alltrim(str(lncount)) 

&& And below, I usually like to specify SHARED or 
&& EXCLUSIVE and not count on the EXCLUSIVE setting 
&& that you desire to be already set in the environment
 	USE vwmmembership IN 0 ALIAS &cNewAliasName again
	SELECT &cNewAliasName
	SET ORDER TO username
	BROWSE NOINIT nowait
	lncount = lncount + 1
	SKIP
ENDDO