Here's a crocheted afghan that my mother does. It's easy and it's one big piece rather than blocks or strips. I don't know about putting her name on it - just do it in her favorite colors. I wouldn't try to do a quilt block combined with the afghan, because you'd have to quilt the block, and then finish the edges, and then figure out a way to attach the yarn. After all is said and done, the first time you wash it you'll have a misshapen mess because the different components will shrink differently.

Great Granny Rectangular Afghan
Materials: Worsted weight yarn, 16 ounces each Color 1, Color 2, Color 3; 20 ounces Color 4 (Note: because yarn yardages of different brands vary considerably, on a large project such as an afghan it is advisable to buy an extra skein of each color to be sure you have enough of the same dye lot to complete the project); size H crochet hook or size needed for gauge.
Gauge: With H hook, rectangle should measure approximately 5” X 15 ½” after 4th round is worked (the second Color 1 round).
Note: Color sequence is Color 1, Color 2, Color 3, Color 4.
Instructions: This afghan is made differently than the usual granny because it is rectangular rather than square. You will start the rectangle with a foundation row, then begin working in rounds in the same manner that a regular square is worked.
Foundation Row: With Color 1, chain 48. Double crochet in 4th chain from hook, chain 1, skip 1, double crochet in next 3 chains, * chain 1, skip 1, double crochet in next 3 chains. Repeat from * across, ending skip 1, chain 1, half double crochet in last chain. Finish off Color 1.
Round 1: With right side facing, join Color 2 with a slip stitch in chain 1 space at end of previous row, chain 3, work 2 double crochets in same space (chain 1, 3 double crochets) 3 times in same space, 3 double crochets in each space between groups to chain space at opposite end of Foundation Row, work (3 double crochets, chain 1) 4 times in end space, continue around working 3 double crochets in each space between groups. Join with a slip stitch, finish off Color 2.
Round 2: Hold rectangle with right side facing and narrow end at top. Join Color 3 with a slip stitch in chain 1 corner space at right hand side of top. Chain 3, (2 double crochet, chain 1, 3 double crochets) all in same space (corner made); 3 double crochets between next 2 groups of double crochets (for end); (3 double crochets, chain 1, 3 double crochets) all in next chain 1 space (corner made); 3 double crochets between each group along side; (3 double crochets, chain 1, 3 double crochets) in next corner chain 1 space; 3 double crochets between next 2 groups; (3 double crochets, chain 1, 3 double crochets) all in next chain 1 space; 3 double crochets between each group along remaining side, join with a slip stitch to starting chain; finish off Color 3.
Round 3: Again holding rectangle with right side facing and narrow end at top, join Color 4 with a slip stitch in chain 1 space of upper right corner; chain 3, 2 double crochets, chain 1, 3 double crochets in space; * 3 double crochets between each group along side, (3 double crochets, chain 1, 3 double crochets) in chain 1 space of next corner; repeat from * 3 times, 3 double crochets between each group along last side, join with a slip stitch to starting chain. Finish off Color 4.
From now on: Continue to repeat Round 3, working 2 rounds in each color, then 3 rounds in each color; then 4 rounds in each color, etc. Work 2 more rounds in Color 4 to finish.
Fringe: We put 1 tassel in each corner space and in each space between groups along the 2 narrow ends, a total of 58 tassels on each side. For each tassel you need 8 strands of Color 4, cut to 14” lengths. Hold all 8 strands together, fold in half. With crochet hook and wrong side of afghan facing you, pull folded end through corner or space, pull loose ends through folded end, and pull knot up tightly. Repeat in each space and each corner.