Madison is the number two choice of girls' names for 2003. That means that by the time your daughter enters school there will be many other Madison's around.
Elyse is very pretty. I think there would be pronunciation problems with Alysse.
Here are the top 100 for 2003:
1. Emily 2. Madison 3. Hannah
4. Emma 5. Alexis 6. Ashley
7. Abigail 8. Sarah 9. Samantha
10. Olivia 11. Elizabeth 12. Alyssa
13. Lauren 14. Isabella 15. Grace
16. Jessica 17. Brianna 18. Taylor
19. Kayla 20. Anna 21. Victoria
22. Megan 23. Sydney 24. Chloe
25. Rachel 26. Jasmine 27. Sophia
28. Jennifer 29. Morgan 30. Natalie
31. Julia 32. Kaitlyn 33. Hailey
34. Destiny 35. Haley 36. Katherine
37. Nicole 38. Alexandra 39. Maria
40. Savannah 41. Stephanie 42. Mia
43. Mackenzie 44. Allison 45. Amanda
46. Jordan 47. Jenna 48. Faith
49. Paige 50. Makayla 51. Andrea
52. Mary 53. Brooke 54. Katelyn
55. Rebecca 56. Madeline 57. Michelle
58. Kaylee 59. Sara 60. Kimberly
61. Zoe 62. Kylie 63. Aaliyah
64. Sierra 65. Amber 66. Caroline
67. Gabriella 68. Vanessa 69. Alexa
70. Trinity 71. Danielle 72. Erin
73. Autumn 74. Angelina 75. Shelby
76. Gabriella 77. Riley 78. Jada
79. Lily 80. Melissa 81. Jacqueline
82. Angela 83. Ava 84. Isabel
85. Bailey 86. Ariana 87. Jade
88. Melanie 89. Courtney 90. Leah
91. Maya 92. Ella 93. Jocelyn
94. Leslie 95. Claire 96. Christina
97. Lillian 98. Evelyn 99. Gabriela
100. Catherine
http://www.bellaonline.com/articles/art13683.asp