The shrub looks like a leucothoe. Unfortunately, leucothoe is very prone to various fungal leaf spot diseases. Most of these diseases are cosmetic but they are very unsightly.
Fungal diseases are worse when conditions are wet and plants do not have good air circulation around them. Removing the diseased leaves is advisable including raking any that are lying underneath or near the shrub. A fungicide will not cure the disease but could help protect the new growth. But, even if you use a fungicide, you may continue to get leaf spot especially in wet years.
Please see the following information from our website,
We notice that there is a downspout/cleanout near the plants and it looks like some erosion of the mulch. Check the drainage in the area and make sure the spout is not dumping water in the root zone. Mulch should be no thicker than several inches and away from the base of the shrub.