Way to rename a follower

Any follower that is skilled at light armor and sneak (and optionally, archery too) should be fine. Followers should preferably be non-mage, as casting spells will attract enemies and blow your cover. Complete list of followers and their descriptions here: http://uesp.net/wiki/Skyrim:Followers

Followers that are good at sneak, light armor and archery are: Aela the Huntress, Cicero and Dark Brotherhood Initiate.

Tips to make followers extra-sneaky:

• Have them wear light armor only, as heavy armor is noisier and makes them more likely to be detected.
• Give him/her an item that has the Muffle (wearer is muffled and moves silently) effect (usually a boot or a shoe; and usually light armor too).
• Have you follower wear apparel that increases sneak skill (Fortify Sneak).

Also, note that (from the UESP wiki's "Skyim Followers - Follower Stats" article):

A follower levels up according to the PC's level up to the follower's maximum level (which varies for each). With few exceptions, each follower has a maximum level, and a specific set of primary skills, which are dictated by their class.

Prior to patch 1.6, a follower's skills, health, and other stats were set when they were first spawned (which is typically when you enter their starting cell, become a Thane, and so on) and would not increase as their level increased. Prior to the fixing of this failure of stats to update with patch 1.6, players could update a non-essential follower's stats so they would increase based on their current level by using the Wabbajack to polymorph them into another creature, after which their stats would update upon recovering their original form. Players of the PC version could also use certain console commands to fix any follower's inability to update their stats with each level.

So in most cases, leveling up the player character will also make your follower level up, increasing the follower's sneak skill (the maximum and by how much, will depend on the specific follower and their NPC class).

Having completed the "Innocence Lost" quest, I immediately fast traveled to my house in Whiterun and slept for 1 hour, the kidnapping took place straight away, there was no delay.

It has been noted on the wiki that:

If the courier doesn't appear after waiting a few days, sleep in a bed for at least 8 hours and the quest will continue.

• Sometimes this can take several days, even with sleeping.
• If the courier still does not appear, try fast traveling to a different hold and waiting.
• Sleeping for at least 8 hours is not necessary. 5 hours continued the quest. (PC) 1 hour continued the quest. (Xbox 360) 1 hour worked (PS3)

Just keep wandering around a different town and waiting until the courier arrives, it's been suggested this can take many days in game.