DUMPFILE=mydump.sql
grep "^USE " ${DUMPFILE} | sed 's/;//' | sed 's/`//g' | awk '{print $2}'

EXAMPLE

# grep "^USE " dump.sql | sed 's/;//' | sed 's/`//g' | awk '{print $2}'
CR1281653
CR1289379
MasterDB
ProjectDB
TPLB23
a110107
a110107_copy
cardfree_orders_lab
mysql
nulldatetest
part_lab
part_test
partition_engine
redwards
scmp_lab
topup_lab
wsms2_lab
zenith_lab
CR1281653
CR1289379
MasterDB
ProjectDB
TPLB23
a110107
a110107_copy
cardfree_orders_lab
mysql
nulldatetest
part_lab
part_test
partition_engine
redwards
scmp_lab
topup_lab
wsms2_lab
zenith_lab
root@vt-mysql:~/TPLB-23#

PROPOSED SOLUTION

DUMPFILE=mydump.sql
grep "^USE " ${DUMPFILE} | sed 's/;//' | sed 's/`//g' | awk '{print $2}'

EXAMPLE

# grep "^USE " dump.sql | sed 's/;//' | sed 's/`//g' | awk '{print $2}'
CR1281653
CR1289379
MasterDB
ProjectDB
TPLB23
a110107
a110107_copy
cardfree_orders_lab
mysql
nulldatetest
part_lab
part_test
partition_engine
redwards
scmp_lab
topup_lab
wsms2_lab
zenith_lab
CR1281653
CR1289379
MasterDB
ProjectDB
TPLB23
a110107
a110107_copy
cardfree_orders_lab
mysql
nulldatetest
part_lab
part_test
partition_engine
redwards
scmp_lab
topup_lab
wsms2_lab
zenith_lab
#

You could collect them in a variable (Note: You must escape the backquote)

# DBLIST=`grep "^USE " dump.sql | sed 's/;//' | sed 's/\`//g' | awk '{print $2}'`
# echo ${DBLIST}
CR1281653 CR1289379 MasterDB ProjectDB TPLB23 a110107 a110107_copy cardfree_orders_lab mysql nulldatetest part_lab part_test partition_engine redwards scmp_lab topup_lab wsms2_lab zenith_lab CR1281653 CR1289379 MasterDB ProjectDB TPLB23 a110107 a110107_copy cardfree_orders_lab mysql nulldatetest part_lab part_test partition_engine redwards scmp_lab topup_lab wsms2_lab zenith_lab
#

GIVE IT A TRY !!!