Learn English – Word for children that have a babysitter or au pair

The word namefellow or name-fellow, although rather obscure, does have exactly the meaning you're after, without the connotation of namesake that both people are named after the same person.

In Tristram of Lyonesse (1882) by the poet A.C. Swinburne, the protagonist travels to Brittany where he meets another knight named Tristram:

But by the sea-banks where at morn their foes
Might find them, lay those knightly name-fellows,
One sick with grief of heart and sleepless, one
With heart of hope triumphant as the sun

• Browsing - Surveying goods for sale in a leisurely and casual way.

• Perusing - Examining carefully or at length.

• Window Shopping - The activity of looking at goods displayed in shop windows, especially without intending to buy anything.

These could all apply to your situation, depending on what you want to focus on and portray.