Whatever item you use, when you use it enough times, you'll become more proficient with it.
Is there a way to customize these items to make it totally yours?

Of course there is. You can upgrade them.

Among equipment, any equipment that is either worn on the body or handheld have a stat called Proficiency.

These items can be upgraded after gaining some Proficiency.

In terms of the familiarity with the item, it's important to note that an older character is bound to rack up familiarity much faster than a younger character.

Upgrades can be done in a number of ways.

In some instances, if one aspect of the item is upgraded, then the other upgrades won't be available for that particular item.

The NPC that modifies items differ depending on the item you'd like to modify, so it's imperative that you find the right NPC for the item.

You don't have to upgrade your items at the Clothing Shop or the Blacksmith's.
Usually, the items are upgraded by the best NPCs of that particular item, so it doesn't hurt to ask around.

For clothes and armors, upgrading means, among other things, altering them to fit your body. Once it's upgraded, it can't be worn by anyone else.

Upgrade your items to overcome the weaknesses while enhancing the strengths, and you'll find yourself using items that are much more valuable than those sold in stores.
Use this well, and hopefully you'll find an item that fits you...like a nicely-upgraded glove.